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NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers

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NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers

Edited By Ramraj Saini | Updated on Nov 29, 2023 04:53 PM IST

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers provided here. These NCERT solutions are prepared by expert team at careers360 with considering the latest CBSE syllabus 2023. The chapter starts with problems that introduce the concepts of multiples and divisors. As it progresses, multiples, divisors, and factors add fun to the chapter in the form of a game. CBSE NCERT solutions for Class 6 Maths chapter 3 Playing with Numbers is covering the Class 6 NCERT solution from each concept. In chapter 3 Playing with Numbers, students will learn about prime and composite numbers, tests for divisibility of numbers, and more.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers
NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers

Students must also refer to the NCERT Class 6 Maths Book and cover all the topics diligently. In this particular chapter, there are a total of 7 exercises with a total of 55 questions of NCERT. In addition to this, it is advisable that students must complete NCERT Class 6 Maths Syllabus on time. These solutions are covering all the 55 questions. NCERT Solutions can be a good tool for your preparation if you make its full use.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers - Important Formula

  1. Natural numbers: 1, 2, 3, 4, 5, 6, and so on.
  2. Whole numbers: 0, 1, 2, 3, 4, 5, 6, and so on.
  3. The smallest natural number is 1, and the smallest whole number is 0.
  4. A number line is a line where we mark equally spaced points to represent whole numbers, starting from zero and going on in both positive and negative directions.
  5. Divisibility rules:

    • A number is divisible by 2 if its unit digit is 0, 2, 4, 6, or 8.

    • A number is divisible by 3 if the sum of its digits is divisible by 3.

    • A number is divisible by 4 if the digits in its tens and units place are divisible by 4.

    • A number is divisible by 5 if its unit digit is 0 or 5.

    • A number is divisible by 6 if it satisfies the divisibility rules for both 2 and 3.

    • A number is divisible by 8 if the number formed by its hundreds, tens, and units placed is divisible by 8.

    • A number is divisible by 9 if the sum of its digits is divisible by 9.

    • A number is divisible by 10 if its units place digit is 0.

    • A number is divisible by 11 if the difference between the sum of its digits in odd places and the sum of its digits in even places is either 0 or divisible by 11.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers - Important Topics

Multiples: In mathematics, multiples are numbers that can be divided by another number without leaving a remainder. For example, multiples of 3 include 3, 6, 9, 12, and so on.

Divisors: Divisors are numbers that divide another number evenly, without leaving a remainder. For example, the divisors of 12 are 1, 2, 3, 4, 6, and 12.

Factors: Factors are the numbers that divide a given number evenly, without leaving a remainder. They are the divisors of a number. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

(a) A factor of a number is an exact divisor of that number: This means that a factor divides the given number without leaving any remainder.

(b) Every number is a factor of itself. 1 is a factor of every number: Every number is divisible by itself, and 1 divides every number without leaving a remainder.

(c) Every factor of a number is less than or equal to the given number: The factors of a number are always smaller than or equal to the given number.

(d) Every number is a multiple of each of its factors: If a number is a factor of another number, then the second number is a multiple of the first number. For example, 2 is a factor of 8, and 8 is a multiple of 2.

(e) Every multiple of a given number is greater than or equal to that number: When you multiply a number by a factor, the result is always greater than or equal to the original number.

(f) Every number is a multiple of itself: Any number multiplied by 1 gives the same number, so every number is a multiple of itself.

Prime Numbers and Composite Numbers:

(a) Prime Number: A prime number is a number greater than 1 that has no divisors other than 1 and itself. In other words, a prime number has exactly two factors. For example, 2, 3, 5, 7, 11 are prime numbers.

(b) Composite Number: A composite number is a number greater than 1 that has more than two factors. In other words, a composite number has factors other than 1 and itself. For example, 4, 6, 8, 9, 12 are composite numbers.

(c) Co-prime Numbers: Co-prime numbers are two numbers that have only 1 as their common factor. In other words, the greatest common factor (GCF) of co-prime numbers is 1.

(d) Divisibility Rules: Divisibility rules are specific patterns or tests that help determine if a number is divisible by another number without performing actual division. These rules provide a quick way to check divisibility by small numbers. Some examples include divisibility by 2 (if the last digit is even), 3 (if the sum of digits is divisible by 3), 4 (if the last two digits form a number divisible by 4), 5 (if the last digit is 0 or 5), and so on.

Highest Common Factor (HCF): The highest common factor, also known as the greatest common divisor (GCD), of two or more numbers is the largest number that divides each of them without leaving a remainder. For example, the HCF of 12 and 18 is 6.

Lowest Common Multiple (LCM): The lowest common multiple of two or more numbers is the smallest multiple that is divisible by each of the given numbers. For example, the LCM of 4 and 6 is 1

Free download NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers PDF for CBSE Exam.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Number

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NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers (Intext Questions and Exercise)

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Topic: Factors and Multiples

Q Find the possible factors of 45, 30, and 36.

Answer: The possible factor of

45=1,3,5,9,15,45
30=1,2,3,5,6,10,15,30
36=1,2,3,4,6,9,12,18,36


NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise: 3.1

Q1 Write all the factors of the following numbers :
(a) 24 (b) 15 (c) 21 (d) 27 (e) 12
(f) 20 (g) 18 (h) 23 (i) 36

Answer: (a) 24 = 1 \times 24

= 2 \times 12

= 3 \times 8

= 4 \times 6

Hence Factor of 24 = 1, 2, 3, 4, 6, 8, 12 and 24 itself.

(b) 15 = 1 \times 15

= 3 \times 5

= 5 \times 3

Hence factor of 15 = 1, 3, 5 and 15.

(c) 21 = 1 \times 21

= 3 \times 7

= 7 \times 3

Hence factor of 21 = 1, 3, 7 and 21.

(d) 27 = 1 \times 27

= 3 \times 9

= 9 \times 3

Hence Factor of 27 are 1, 3, 9 and 27.

(e) 12=1 \times 12

=2 \times 6

=3 \times 4

=4 \times 3

Hence Factors of 12 are 1,2,3,4,6, and 12
(f) 20 = 1 \times 20

= 2 \times 10

= 4 \times 5

= 5 \times 4

Hence Factors of 20 are 1, 2, 4, 5, 10, and 20.

(g) 18 = 1 \times 18

= 2 \times 9

= 3 \times 6

Hence Factors of 18 are 1, 2, 3, 6, 9 and 18.

(h) 23 = 1 \times 23

= 23 \times 1

Hence factors of 23 are 1 and 23.

(i) 36 = 1 \times 36

= 2 \times 18

= 3 \times 12

= 4 \times 9

= 6 \times 6

Hence factors of 36 are 1, 2, 3, 4, 6, 9, 18 and 36.

Q2 Write first five multiples of :
(a) 5 (b) 8 (c) 9

Answer: First Five multiple of

(a) 5

5 \times 1 = 5

5 \times 2 = 10

5 \times 3 = 15

5 \times 4 = 20

5 \times 5 = 25

(b) 8

8 \times 1 = 8

8 \times 2 = 16

8 \times 3 = 24

8 \times 4 = 32

8 \times 5 = 40

(c) 9

9 \times 1 = 9

9 \times 2 = 18

9 \times 3 = 27

9 \times 4 = 36

9 \times 5 = 45

Q3 Match the items in column 1 with the items in column 2.
Column 1 Column 2
(i) 35 (a) Multiple of 8
(ii) 15 (b) Multiple of 7
(iii) 16 (c) Multiple of 70
(iv) 20 (d) Factor of 30
(v) 25 (e) Factor of 50
(f) Factor of 20

Answer: Column 1 Column 2

(i) 35 (b) Multiple of 7

(ii) 15 (d) Factor of 30

(iii) 16 (a) Multiple of 8

(iv) 20 (d) Factor of 20

(v) 25 (e) Factor of 50

Q4 Find all the multiples of 9 up to 100.

Answer: Multiples of 9 up to 100 are:

9 \times 1 = 9

9 \times 2 = 18

9 \times 3 = 27

9 \times 4 = 36

9 \times 5 = 45

9 \times 6 = 54

9 \times 7 = 63

9 \times 8 = 72

9 \times 9 = 81

9 \times 10 = 90

9 \times 11 = 99

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Topic: Prime and Composite Numbers

Q1 Observe that 2 × 3 + 1 = 7 is a prime number. Here, 1 has been added to a multiple of 2 to get a prime number. Can you find some more numbers of this type?

Answer: some more numbers of this type are :

2 \times 2+1=5
2 \times 5+1=11
2 \times 6+1=13

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise: 3.2

Q1 What is the sum of any two (a) Odd numbers? (b) Even numbers?

Answer: (a) the sum of any two Odd numbers is always even. for e.g. 3 + 5 = 8 and 9 + 7 = 16

(b) the sum of any two Even numbers is always even. for e.g. 2 + 4 = 6 and 8 + 4 = 12

Q2 State whether the following statements are True or False:
(a) The sum of three odd numbers is even.
(b) The sum of two odd numbers and one even number is even.
(c) The product of three odd numbers is odd.
(d) If an even number is divided by 2, the quotient is always odd.
(e) All prime numbers are odd.
(f) Prime numbers do not have any factors.
(g) The sum of two prime numbers is always even.
(h) 2 is the only even prime number.
(i) All even numbers are composite numbers.
(j) The product of two even numbers is always even.

Answer: (a) False, Because the sum of two odd numbers is even and the sum of even number and an odd number is odd, so the sum of three odd numbers is odd.

for example :

3 + 5 + 7 = 15, i.e., odd

(b) True, as the sum of two odd number is even a sum of two even number is even.

for example :

3 + 5 + 6 = 14, i.e., even

(c) True because the product of two odd numbers is odd and product of any number(odd or even) with an even number is even.

For example :

3 x 5 x 7 = 105, i.e., odd

(d) False, because it is possible to have a quotient even when divided by 2

for example :

4÷2=24÷2=2, i.e., even

(e) False as 2 is a prime number and it is also even

(f) False as 1 and the number itself are factors of the number

(g) False for example

2 + 3 = 5 , i.e., odd

(h) True

(i) False as 2 is a prime number

(j) True .

Q4 Write down separately the prime and composite numbers less than 20.

Answer: Prime numbers less than 20 are : 2, 3, 5, 7, 11, 13, 17, 19

Composite numbers less than 20 are : 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

Q5 What is the greatest prime number between 1 and 10?

Answer: Prime numbers between 1 and 10 are 2, 3, 5, and 7. Among these numbers, 7 is the greatest.

Q6 Express the following as the sum of two odd primes.
(a) 44 (b) 36 (c) 24 (d) 18

Answer: (a) 44 = 37 +7

(b) 36 = 31 +5

(c) 24 = 19 +5

(d) 18 = 11 +7

Q7 Give three pairs of prime numbers whose difference is 2.
[Remark: Two prime numbers whose difference is 2 are called twin primes].

Answer: three pairs of prime numbers whose difference is 2 are :

3,5

41,43 and

71,73

Q8 Which of the following numbers are prime?
(a) 23 (b) 51 (c) 37 (d) 26

Answer: (a) 23,23=1 \times 23,23=23 \times 123,23=1 \times 23,23=23 \times 1 23 has only two factors, 1 and 23. Therefore, it is a prime number.

(b) 51,51=1 \times 51,51=3 \times 1751,51=1 \times 51,51=3 \times 17 51 has four factors, 1, 3, 17, 51. Therefore, it is not a prime number. It is a composite number.

(c) 37 It has only two factors, 1 and 37. Therefore, it is a prime number.

(d) 26 26 has four factors (1, 2, 13, 26). Therefore, it is not a prime number. It is a composite number.

Q9 Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Answer: Seven consecutive composite numbers less than 100 so that there is no prime number between them are :

Between 89 and 97, both of which are prime numbers, there are 7 composite numbers. They are: 90,91,92,93,94,95,96

Q10 Express each of the following numbers as the sum of three odd primes:
(a) 21 (b) 31 (c) 53 (d) 61

Answer: (a) 21 = 3 + 7 + 11

(b) 31 = 5 + 7 + 19

(c) 53 = 3 + 19 + 31

(d) 61 = 11 + 19 + 31

Q11 Write five pairs of prime numbers less than 20 whose sum is divisible by 5. (Hint : 3+7 = 10)

Answer: Five pairs of prime numbers less than 20 whose sum is divisible by 5 are :

2+3=5

2+13=15

3+17=20

7+13=20

19+11=30


NCERT solutions for class 6 maths chapter 3 Playing with numbers Exercise: 3.3

Q1 Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10 ; by 11 (say, yes or no):

Number
Divisible by
2
3
4
5
6
8
9
10
11
128
Yes
No
Yes
No
No
Yes
No
No
No
990
......
......
......
......
......
......
......
......
......
1586
......
......
......
......
......
......
......
......
......
275
......
......
......
......
......
......
......
......
......
6686
......
......
......
......
......
......
......
......
......
639210
......
......
......
......
......
......
......
......
......
429714
......
......
......
......
......
......
......
......
......
2856
......
......
......
......
......
......
......
......
......
3060
......
......
......
......
......
......
......
......
......
406839
......
......
......
......
......
......
......
......
......

Answer:

Number
Divisible by
2
3
4
5
6
8
9
10
11
128
Yes
No
Yes
No
No
Yes
No
No
No
990
Yes
Yes
No
Yes
Yes
No
Yes
Yes
Yes
1586
Yes
No
No
No
No
No
No
No
No
275
No
No
No
Yes
No
No
No
No
Yes
6686
Yes
No
No
No
No
No
No
No
No
639210
Yes
Yes
No
Yes
Yes
No
No
Yes
Yes
429714
Yes
Yes
No
No
Yes
No
Yes
No
No
2856
Yes
Yes
Yes
No
Yes
Yes
No
No
No
3060
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
No
406839
No
Yes
No
No
No
No
No
No
No


Q2 Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:
(a) 572 (b) 726352 (c) 5500 (d) 6000 (e) 12159
(f) 14560 (g) 21084 (h) 31795072 (i) 1700 (j) 2150

Answer: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.

A number with 3 or more digits is divisible by 8 if the number formed by its last three digits is divisible by 8.


a) 572

72 is divisible by 4, hence the number is divisible by 4.

The number is not divisible by 8.


b) 726352

52 is divisible by 4, hence the number is divisible by 4.

352 is divisible by 8, hence the number is divisible by 8.


c) 5500

0 is divisible by 4, hence the number is divisible by 4.

500 is not divisible by 8, hence the number is not divisible by 8.


d) 6000

0 is divisible by 4 and 8. Hence, the number is divisible by 4 and 8.


e) 12159

59 is not divisible by 4. Hence, the number is not divisible by 4.

159 is not divisible by 8, hence the number is not divisible by 8.


f) 14560

60 is divisible by 4, hence the number is divisible by 4.

560 is divisible by 8, hence the number is divisible by 8.


g) 21084

84 is divisible by 4, hence the number is divisible by 4.

84 is not divisible by 8, hence the number is not divisible by 8.


h) 31795072

72 is divisible by 4 and 8. Hence the number is divisible by 4 and 8.


i) 1700

The number is divisible by 4.

700 is not divisible by 8, hence the number is not divisible by 8.


j) 2150

50 is not divisible by 4, hence the number is not divisible by 4.

150 is not divisible by 8, hence the number is not divisible by 8.

Q3 Using divisibility tests, determine which of the following numbers are divisible by 6:
(a) 297144 (b) 1258 (c) 4335 (d) 61233 (e) 901352
(f) 438750 (g) 1790184 (h) 12583 (i) 639210 (j) 17852

Answer: (a) 297144

Since the last digit Of the number is 4, it is divisible by 2. On adding all the digits of the number, the sum obtained is 27. Since 27 is divisible by 3, the given number is also divisible by 3. As the number is divisible by both 2 and 3, it is divisible by 6.

(b) 1258

Since the last digit of the number is 8, it is divisible by 2. On adding all the digits of the number, the sum obtained is 16. Since 16 is not divisible by 3, the given number is also not divisible by 3. As the number is not divisible by both 2 and 3, it is not divisible by 6.

(c) 4335

The last digit of the number is 5, which is not divisible by 2. Therefore, the given number is also not divisible by 2. On adding all the digits of the number, the sum obtained is 15. Since 15 is divisible by 3, the given number is also divisible by 3. As the number is not divisible by both 2 and 3, it is not divisible by 6.

(d) 61233

The last digit of the number is 3, which is not divisible by 2. Therefore, the given number is also not divisible by 2. On adding all the digits Of the number, the sum obtained is 15. Since 15 is divisible by 3, the given number is also divisible by 3. As the number is not divisible by both 2 and 3, it is not divisible by 6.

(e) 901352

Since the last digit of the number is 2, it is divisible by 2. On adding all the digits of the number, the sum obtained is 20. Since 20 is not divisible by 3, the given number is also not divisible by 3. As the number is not divisible by both 2 and 3, it is not divisible by 6.

(f) 438750

Since the last digit of the number is O, it is divisible by 2. On adding all the digits of the number, the sum obtained is 27. Since 27 is divisible by 3, the given number is also divisible by 3. As the number is divisible by both 2 and 3, it is divisible by 6.

(g) 1790184

Since the last digit of the number is 4, it is divisible by 2. On adding all the digits of the number, the sum obtained is 30. Since 30 is divisible by 3, the given number is also divisible by 3. As the number is divisible by both 2 and 3, it is divisible by 6.

(h) 12583

Since the last digit of the number is 3, it is not divisible by 2. On adding all the digits of the number, the sum obtained is 19. Since 19 is not divisible by 3, the given number is also not divisible by 3. As the number is not divisible by both 2 and 3, it is not divisible by 6.

(i) 639210

Since the last digit of the number is O, it is divisible by 2. On adding all the digits of the number, the sum obtained is 21. Since 21 is divisible by 3, the given number is also divisible by 3. As the number is divisible by both 2 and 3, it is divisible by 6.

(j) 17852

Since the last digit of the number is 2, it is divisible by 2. On adding all the digits of the number, the sum obtained is 23. Since 23 is not divisible by 3, the given number is also not divisible by 3. As the number is not divisible by both 2 and 3, it is not divisible by 6.

Q4 Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001
(f) 901153

Answer: (a) 5445

Sum of the digits at odd places = 5 + 4 = 9 Sum of the digits at even places = 4 + 5 = 9 Difference = 9 - 9 = 0 As the difference between the sum of the digits at odd places and the sum of the digits at even places is O, therefore, 5445 is divisible by 11.

(b) 10824

Sum of the digits at odd places = 4 + 8 + 1 = 13 Sum of the digits at even places = 2 + 0 = 2 Difference = 13 - 2 = 11 The difference between the sum of the digits at odd places and the sum of the digits at even places is 11, which is divisible by 11. Therefore, 10824 is divisible by 11.

(c) 7138965

Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24 Sum of the digits at even places =6 + 8 + 1 = 15 Difference = 24 - 15 = 9 The difference between the sum of the digits at odd places and the sum of digits at even places is 9, which is not divisible by 11. Therefore, 7138965 is not divisible by 11.

(d) 70169308

Sum of the digits at odd places = 8 + 3 + 6 + 0 Sum of the digits at even places = 0 + 9 + 1 + 7 = 17 Difference = 17 - 17 = 0 As the difference between the sum of the digits at odd places and the sum of the digits at even places is O, therefore, 70169308 is divisible by 11.

(e) 10000001

Sum Of the digits at Odd places = 1 Sum of the digits at even places 1 Difference = 1 - 1 = 0 As the difference between the sum of the digits at odd places and the sum of the digits at even places is O, therefore, 10000001 is divisible by 11.

(f) 901153

Sum of the digits at odd places = 3 + 1 + 0 = 4 Sum Of the digits at even places = 5 + 1 + 9 = 15 Difference = 15 - 4 = 11 The difference between the sum of the digits at odd places and the sum of the digits at even places is 11, which is divisible by 11. Therefore, 901153 is divisible by 11.

Q5 Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3 : (a) __ 6724 (b) 4765 __ 2

Answer: (a) _6724

Sum of the remaining digits = 19

To make the number divisible by 3, the sum of its digits should be divisible by 3. The smallest multiple of 3 which comes after 19 is 21.

Therefore,

smallest number = 21 - 19 - 2

Now, 2 + 3 + 3 = 8 If we put 8, then the sum of the digits will be 27 and as 27 is divisible by 3, the number will also be divisible by 3.

Therefore, the largest number is 8.

(b) 4765_2

Sum of the remaining digits = 24

To make the number divisible by 3, the sum of its digits should be divisible by 3. As 24 is already divisible by 3, the smallest number that can be placed here is 0.

Now, 0 + 3 = 3 3 + 3 = 6 3 + 3 + 3 = 9

How ever, 3 + 3 + 3 + 3 = 12

If we put 9, then the sum of the digits will be 33 and as 33 is divisible by 3, the number will also be divisible by 3.

Therefore, the largest number is 9.

Q6 Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11 : (a) 92 __ 389 (b) 8 __ 9484.

Answer: (a) 92 __ 389

Sum of odd digits = 9 + (blank space) + 8 = 17 + blank space

Sum of even digits = 2 + 3 + 9 = 14

As we know,

The number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11.

If we make the sum of odd digits = 25

then we will have difference = 25 - 14 = 11

which is divisible by 11.

To make the sum of odd digits = 25,

the number at black space would be 8.

(b) 8 __ 9484

Sum of odd digits = 8 + 9 + 8 = 25

Sum of even digits = blank space + 4 + 4 = blank space + 8

The number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11.

If we make the sum of even digits = 14 then we will have difference = 25 - 14 = 11 which is divisible by 11.

To make the sum of even digits = 14,

the number at black space would be 6.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Topic: Common Factors and Common Multiples

Q Find the common factors of:
(a) 8, 20 (b) 9, 15

Answer: The common factors of the following are:
(a) 8, 20

8 = 2\times2\times2\times2

20 = 2\times2\times5

Hence, the common factors are 1, 2\ and\ (2\times2 = )4

(b) 9, 15

9 = 3\times3

15= 3\times5

Hence, the common factors are 1\ and\ 3 .

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise: 3.4

Q1 Find the common factors of :
(a) 20 and 28 (b) 15 and 25 (c) 35 and 50 (d) 56 and 120

Answer: (a) 20 and 28

Factors of 20=1,2,4,5,10,20

Factors of 28=1,2,4,7,14,28

Common factors =1,2,4

(b) 15 and 25

Factors of 15=1,3,5,15

Factors of 25=1,5,25

Common factors =1,5

(c) 35 and 50

Factors of 35=1,5,7,35

Factors of 50=1,2,5,10,25,50

Common factors =1,5

(d) 56 and 120

Factors of 56=1,2,4,7,8,14,28,56

Factors of 120=1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Common factors =1,2,4,8

Q2 Find the common factors of :
(a) 4, 8 and 12 (b) 5, 15 and 25

Answer: (a) 4,8,12

Factors of 4=1,2,4

Factors of 8=1,2,4,8

Factors of 12=1,2,3,4,6,12

Common factors =1,2,4


(b) 5,15, and 25

Factors of 5=1,5

Factors of 15=1,3,5,15

Factors of 25=1,5,25

Common factors =1,5

Q3 Find the first three common multiples of :
(a) 6 and 8 (b) 12 and 18

Answer: (a) 6 and 8

Multiple of 6=6,12,18,24,30…

Multiple of 8=8,16,24,32……

common multiples =24,48,72


(b) 12 and 18

Multiples of 12=12,24,36,78

Multiples of 18=18,36,54,72 3

common multiples = 36,72,108

Q4 Write all the numbers less than 100 which are common multiples of 3 and 4.

Answer: Multiples of 3 = 3,6,9,12,15…

Multiples of 4 = 4,8,12,16,20…

Common multiples = 12,24,36,48,60,72,84,96

Q5 Which of the following numbers are co-prime?
(a) 18 and 35 (b) 15 and 37 (c) 30 and 415
(d) 17 and 68 (e) 216 and 215 (f) 81 and 16

Answer: (a) 18 and 35

Factors of 18=1,2,3,6,9,18

Factors of 35=1,5,7,35

Common factor =1

Therefore, the given two numbers are co-prime.


(b)15 and 37

Factors of 15=1,3,5,15

Factors of 37=1,37

Common factors =1

Therefore, the given two numbers are co-prime.


(c) 30 and 415

Factors of 30=1,2,3,5,6,10,15,30

Factors of 415=1,5,83,415

Common factors =1,5

As these numbers have a common factor other than 1, the given two numbers are non co-prime.


(d) 17 and 68

Factors of 17=1,17

Factors of 68=1,2,4,17,34,68

Common factors =1,17

As these numbers have a common factor other than 1, the given two numbers are non co-prime.


(e) 216 and 215

Factors of 216=1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216

Factors of 215=1,5,43,215

Common factors =1

Therefore, the given two numbers are co-prime.


(f) 81 and 16

Factors of 81=1,3,9,27,81

Factors of 16=1,2,4,8,16

Common factors =1

Therefore, the given two numbers are co-prime.

Q6 A number is divisible by both 5 and 12. By which other numbers will that number be always divisible?

Answer: Factors of 5=1,5

Factors of 12=1,2,3,4,6,12

As the common factor of these numbers is 1, the given two numbers are coprime and the number will also be divisible by their product, i.e. 60, and the factors of 60=1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Q7 A number is divisible by 12. By what other numbers will that number be divisible?

Answer: Since the number is divisible by 12, it will also be divisible by its factors i.e., 1, 2, 3, 4, 6, 12. Clearly, 1, 2, 3, 4, and 6 are numbers other than 12 by which this number is also divisible.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Topic: Prime Factorization

Q Write the prime factorizations of 16, 28, 38.

Answer: prime factorizations of

16= 2×2×2×2
28= 2×2×7
38= 2×19

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise: 3.5

Q1 Which of the following statements are true?
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) A number is divisible by 18 if it is divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately


Answer: (a) False as 6 is divisible by 3, but not by 9.

(b) True, as 9 = 3 x 3 Therefore, if a number is divisible by 9, then it will also be divisible by 3.

(c) False as 30 is divisible by 3 and 6 both, but it is not divisible by 18.

(d) True as 9 x 10 = 90 Therefore, If a number is divisible by 9 and 10 both, then it will also be divisible by 90.

(e) False as 15 and 32 are co-primes and also composite.

(f) False as 12 is divisible by 4, but not by 8.

(g) True, as 8 = 2 x 4 Therefore if a number is divisible by 8, then it will also be divisible by 2 and 4.

(h) True as 2 divides 4 and 8 as well as 12. (4 + 8 = 12)

(i) False as 2 divides 12, but not divide 7 and 5.

Q3 Which factors are not included in the prime factorization of a composite number?

Answer: 1 is the factors which are not especially included in the prime factorization of a composite number. When the number is divisible by 2 co-prime numbers then they are divisible by their product.

When two given numbers are divisible by a number, the sum is also divisible by number. When 2 given numbers are divisible by number then its difference is divisible by that number.

Q4 Write the greatest 4-digit number and express it in terms of its prime factors.

Answer: Greatest four-digit number = 9999

9999 = 3 \times 3 \times 11 \times 101

Q5 Write the smallest 5-digit number and express it in the form of its prime factors.

Answer: Smallest five-digit number = 10,000

10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5

Q6 Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.

Answer: Prime factors of 1729 are -7,13,19.
Ascending order =7<13<19.
Relation = 7,13,19 differ by 6

Q7 The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

Answer: 2 \times 3 \times 4=24, which is divisible by 6

9 \times 10 \times 11=990, which is divisible by 6

20 \times 21 \times 22=9240, which is divisible by 6

Q8 The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.

Answer: 3+5=8, which is divisible by 4

15+17=32, which is divisible by 4

19+21=40, which is divisible by 4

Q9 In which of the following expressions, prime factorization has been done?
(a) 24 = 2 \times 3 \times 4 (b) 56 = 7 \times 2 \times 2 \times 2
(c) 70 = 2 \times 5 \times 7 (d) 54 = 2 \times 3 \times 9

Answer: in factorization, we don't write composite numbers. All the factors should be prime numbers in this method.

(a) 24 = 2 \times 3 \times 4

As we know that 4 is a composite number.
Hence This is not a prime factorization.

b) 56 = 7 \times 2 \times 2 \times 2
In this factorization, all the factors of 56 are prime numbers. There is no composite number.
Hence This is prime factorization.

c) 70 = 2 \times 5 \times 7
In this factorization, all the factors of 70 are prime numbers. There is not a composite number in this process of factorization.
Hence This is prime factorization.

d) 54 = 2 \times 3 \times 9
In this factorization, 54 is written as the product of 2, 3 and 9. In this factorization, 2 and 3 are prime numbers, but 9 is a composite number.
Hence This is not a prime factorization.

Q10 Determine if 25110 is divisible by 45.
[Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9].

Answer: 45 = 5 \times 9

Factors of 5 = 1, 5

Factors of 9 = 1. 3, 9

Therefore, 5 and 9 are co-prime numbers.

Since the last digit of 25110 is 0. it is divisible by 5.

Sum of the digits of 25110 = 2 + 5 + 1 +1 + 0 = 9

As the sum of the digits of 25110 is divisible by 9, therefore. 25110 is divisible by 9.

Since the number is divisible by 5 and 9 both, it is divisible by 45.

Q12 I am the smallest number, having four different prime factors. Can you find me?

Answer: Since it is the smallest number of such type, it will be the product of 4 smallest prime numbers. that is

2 \times 3 \times 5 \times 7 = 210

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Topic: Highest Common Factor

Q Find the HCF of the following:
(i) 24 and 36 (ii) 15, 25 and 30
(iii) 8 and 12 (iv) 12, 16 and 28

Answer: (i) 24 and 36

24 = 2 \times 2 \times 2 \times 3

36 = 2 \times 2 \times 3 \times 3

HCF = 2 \times 2 \times 3 = 12

(ii) 15, 25 and 30

15 = 3 \times 5

25 = 5 \times 5

30 = 2 \times 3 \times 5

HCF = 5

(iii) 8 and 12

8 = 2 \times 2 \times 2

12 = 2 \times 2 \times 3

HCF = 2 \times 2 = 4

(iv) 12, 16 and 28

12 = 2 \times 2 \times 3

16 = 2 \times 2 \times 2 \times 2

28 = 2 \times 2 \times 7

HCF = 2 \times 2 = 4

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise: 3.6

Q1 Find the HCF of the following numbers :
(a) 18, 48 (b) 30, 42
(c) 18, 60 (d) 27, 63
(e) 36, 84 (f) 34, 102
(g) 70, 105, 175 (h) 91, 112, 49
(i) 18, 54, 81 (j) 12, 45, 75

Answer: (a) 18, 48

18 = 2 x 3 x 3

48 = 2 x 2 x 2 x 2 x 3

HCF = 2 x 3 =6


(b) 30, 42

30 = 2 x 3 x 5

42 = 2 x 3 x 7

HCF = 2 x 3 =6


(c) 18, 60

18 = 2 x 3 x 3

60 = 2 x 2 x 3 x 5

HCF = 2 x 3 = 6


(d) 27, 63

27 = 3 x 3 x 3

63 = 3 x 3 x 7

HCF = 3 x 3 = 9


(e) 36, 84

36 = 2 x 3 x 3 x 3

84 = 2 x 2 x 3 x 7

HCF = 2 x 2 x 3 = 12


(f) 34, 102

34 = 2 x 17

102 = 2 x 3 x 17

HCF = 2 x 17 = 34


(g) 70, 105, 175

70 = 2 x 5 x 7

105 = 3 x 5 x 7

175 = 5 x 5 x 7

HCF = 5 x 7 = 35


(h)91, 112, 49

91 = 7 x 13

112 = 2 x 2 x 2 x 2 x 7

49 = 7 x 7

HCF = 7


(i) 18, 54, 81

18 = 2 x 3 x 3

54= 2 x 3 x 3 x 3

81 = 3 x 3 x 3 x 3

HCF = 3 x 3 = 9


(j) 12, 45, 75

12 = 2 x 2 x 3

45 = 3 x 3 x 5

75 = 3 x 5 x 5

HCF = 2

Q2 What is the HCF of two consecutive
(a) numbers? (b) even numbers? (c) odd numbers?

Answer: (a) 1 e.g., HCF of 2 and 3 is 1.

(b) 2 e.g., HCF of 2 and 4 is 2.

(c) 1 e.g., HCF of 3 and 5 is 1.

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Exercise: 3.7

Q1 Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.

Answer: Weight of the two bags = 75 kg and 69 kg

Maximum weight :

HCF (75, 69)

75 = 3 \times 5 \times 5

69 = 3 \times 23

HCF = 3

Hence the maximum value of weight which can measure the weight of the fertilizer exact number of times is 3.

Q3 The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

Answer: Length =825cm=3 \times 5 \times 5 \times 11

Breadth =675cm=3 \times 3 \times 3 \times 5 \times 5

Height =450cm=2 \times 3 \times 3 \times 5 \times 5

Longest tape = HCF of 825,675, and 450= 3 \times 5 \times 5

=75cm

Therefore, the longest tape is 75cm.

Q4 Determine the smallest 3-digit number which is exactly divisible by 6, 8 and 12.

Answer: Smallest number = LCM of 6, 8, 12

\begin{array}{|c|c|c|}\hline 2 & {6,8,12} \\ \hline 2 & {3,4,6} \\ \hline 2 & {3,2,3} \\ \hline 3 & {3,1,3} \\ \hline 3 & {1,1,1} \\ \hline\end{array}

We have to find the smallest 3-digit multiple of 24.

It can be seen that

24 \times 4 = 96 and

24 \times 5 = 120.

Hence, the smallest 3-digit number which is exactly divisible by 6, 8, and 12 is 120.

Q5 Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

Answer: CM of 8, 10 and 12

\begin{array}{|c|c|}\hline 2 & {8,10,12} \\ \hline 2 & {4,5,6} \\ \hline 2 & {2,5,3} \\ \hline 3 & {1,5,3} \\ \hline 5 & {1,5,1} \\ \hline\end{array}

LCM = 2 \times 2 \times 2 \times 3 \times 5 = 120

We have to find the greatest 3-digit multiple of 120.

It can be seen that

120 \times 8 = 960 and

120 \times 9 = 1080.

Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.

Q6 The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Answer: The time period after which these lights will change = LCM of 48, 72 and 108

\begin{array}{|c|c|}\hline 2 & {48,72,108} \\ \hline 2 & {24,36,54} \\ \hline 2 & {12,18,27} \\ \hline 2 & {6,9,27} \\ \hline 3 & {1,3,9} \\ \hline 3 & {1,1,3} \\ \hline 3 & {1,1,1} \\ \hline\end{array}

LCM=2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 432

They will change together after every 432 seconds i.e., 7 min 12 seconds.

Hence, they will change simultaneously at 7:07:12 am.

Q7 Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times.

Answer: Maximum capacity of the required tanker =HCF of 403,434,465

403=13 \times 31

434=2 \times 7 \times 31

465=3 \times 5 \times 31

HCF=31

Hence the maximum capacity of a container that can measure the diesel of the three containers the exact number of times is 31.

Q8 Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case.

Answer: LCM of 6, 15, 18
\begin{array}{|c|c|c|}\hline 2 & {6,15,18} \\ \hline 3 & {3,15,9} \\ \hline 3 & {1,5,3} \\ \hline 5 & {1,5,1} \\ \hline & {1,1,1} \\ \hline\end{array}

LCM = 2 \times 2 \times 3 \times 5 = 90

Required number = 90 + 5 = 95

Q9 Find the smallest 4-digit number which is divisible by 18, 24 and 32.

Answer: LCM of 18, 24 and 32

\begin{array}{|c|c|}\hline 2 & {18,24,32} \\ \hline 2 & {9,12,16} \\ \hline 2 & {9,6,8} \\ \hline 2 & {9,3,4} \\ \hline 2 & {9,3,2} \\ \hline 3 & {9,3,1} \\ \hline 3 & {3,1,1} \\ \hline & {1,1,1} \\ \hline\end{array}

LCM = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3

We have to find the smallest 4-digit multiple of 288.

It can be observed that 288 \times 3 = 864 and 288 \times 4 = 1152.

Therefore, the smallest 4-digit number which is divisible by 18, 24, and 32 is 1152.

Q10 Find the LCM of the following numbers :
(a) 9 and 4 (b) 12 and 5 (c) 6 and 5 (d) 15 and 4
Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

Answer: (a) LCM = 2 \times 2 \times 3 \times 3 = 36

\begin{array}{|c|c|}\hline 2 & {9,4} \\ \hline 2 & {9,2} \\ \hline 3 & {9,1} \\ \hline 3 & {3,1} \\ \hline & {1,1} \\ \hline\end{array}

(b) LCM = 2 \times 2 \times 3 \times 5 = 60

\begin{array}{|c|c|}\hline 2 & {12,5} \\ \hline 2 & {6,5} \\ \hline 3 & {3,5} \\ \hline 5 & {1,5} \\ \hline & {1,1} \\ \hline\end{array}

(c) LCM = 2 \times 3 \times 5 = 30

\begin{array}{|c|c|}\hline 2 & {6,5} \\ \hline 3 & {3,5} \\ \hline 5 & {1,5} \\ \hline & {1,1} \\ \hline\end{array}

(d) LCM = 2 \times 3 \times 5 = 30

\begin{array}{|c|c|}\hline 2 & {15,4} \\ \hline 2 & {15,2} \\ \hline 3 & {15,1} \\ \hline 5 & {5,1} \\ \hline & {1} \\ \hline\end{array}

Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers.

When two numbers are co-prime, their LCM is the product of those numbers. Also, in each case, LCM is a multiple of 3.

Q11 Find the LCM of the following numbers in which one number is the factor of the other.
(a) 5, 20 (b) 6, 18 (c) 12, 48 (d) 9, 45
What do you observe in the results obtained?

Answer: (a) LCM = 2 \times 2 \times 5 = 20

\begin{array}{|c|c|}\hline 2 & {5,20} \\ \hline 2 & {5,10} \\ \hline 5 & {5,5} \\ \hline & {1,1} \\ \hline\end{array}

(b) LCM = 2 \times 3 \times 3 = 18

\begin{array}{|c|c|}\hline 2 & {6,18} \\ \hline 3 & {3,9} \\ \hline 3 & {1,3} \\ \hline & {1,1} \\ \hline\end{array}

(c) LCM = 2 \times 2 \times 2 \times 2 \times 3 = 48

\begin{array}{|c|c|}\hline 2 & {12,48} \\ \hline 2 & {6,24} \\ \hline 2 & {3,12} \\ \hline 2 & {3,12} \\ \hline 3 & {3,3} \\ \hline & {1,1} \\ \hline\end{array}

(d) LCM = 3 \times 3 \times 5 = 45

\begin{array}{|c|c|}\hline 3 & {9,45} \\ \hline 3 & {3,15} \\ \hline 5 & {1,5} \\ \hline & {1,1} \\ \hline\end{array}

Yes, it can be observed that in each case, the LCM of the given numbers is the larger number. When one number is a factor of the other number, their LCM will be the larger number.

Playing with Numbers Class 6 Chapter 3-Topics

  • Factors and Multiples
  • Prime and Composite Numbers
  • Test For Divisibility of Numbers
  • Common Factors and Common Multiples
  • Some More Divisibility Rules
  • Prime Factorisation
  • Highest Common Factor
  • Lowest Common Multiple
  • Some Problems on HCF and LCM
Also Check -
NCERT Books and NCERT Syllabus

NCERT Solutions for Class 6 Mathematics Chapter-wise

Chapters No.

Chapters Name

Chapter - 1

Knowing Our Numbers

Chapter - 2

Whole Numbers

Chapter - 3

Playing with Numbers

Chapter - 4

Basic Geometrical Ideas

Chapter - 5

Understanding Elementary Shapes

Chapter - 6

Integers

Chapter - 7

Fractions

Chapter - 8

Decimals

Chapter - 9

Data Handling

Chapter -10

Mensuration

Chapter -11

Algebra

Chapter -12

Ratio and Proportion

Chapter -13

Symmetry

Chapter -14

Practical Geometry

Key features of NCERT Solutions for Class 6 Maths chapter 3

Expertly Crafted Solutions: The NCERT Solutions for Chapter 3 in Class 6 Maths are meticulously crafted to offer students clear and precise explanations for every problem and concept presented in the chapter.

Conceptual Clarity: The solutions for Class 6 Maths Chapter 3 aim to foster conceptual clarity by simplifying complex topics and presenting them in an easily understandable manner, promoting a solid foundation for further learning.

Comprehensive Coverage: Class 6 Maths Chapter 3 solutions cover all essential topics and subtopics comprehensively, ensuring that students gain a thorough grasp of the entire chapter's content.

Exam-Focused Approach: The NCERT Class 6 Maths Chapter 3 solutions adopt an exam-oriented approach, equipping students with valuable techniques and strategies to effectively tackle questions, thus enabling them to perform well in examinations.

NCERT Solutions for Class 6 - Subject Wise

How to Use NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers

  • Learn to differentiate between the multiples and factors.
  • Go through some important concepts given in the NCERT.
  • Take a look through some examples to understand the pattern of solutions for a particular question.
  • Once you are done with all the above-written points then you can directly come to the exercises given in the NCERT Solutions for Class 6 .
  • While doing the question of exercise you can take help of NCERT solutions for Class 6 Maths chapter 3 Playing with Numbers.

Frequently Asked Question (FAQs)

1. Write the Topics that are covered in NCERT Solution Class 6 Maths chapter 3.

Here is the topics are covered in NCERT class 6 maths chapter 3 pdf 

  • Factors and Multiples
  • Prime and Composite Numbers
  • Test For Divisibility of Numbers
  • Common Factors and Common Multiples
  • Some More Divisibility Rules
  • Prime Factorisation
  • Highest Common Factor
  • Lowest Common Multiple
  • Some Problems on HCF and LCM
2. As per the latest CBSE syllabus, which types of numbers are covered in NCERT Solutions for maths class 6 chapter 3?

In chapter 3 maths class 6, as per the latest CBSE syllabus, the following types of numbers are discussed:

  1. Prime numbers
  2. Even numbers
  3. Odd numbers
  4. Whole numbers
  5. Natural numbers
  6. Composite numbers
3. What is the smallest prime number which is even?

2 is the smallest prime number which is even.

4. What is the full form of HCF and LCM ?

The full form of HCF and LCM is

HCF= Highest Common Factor

LCM= Lowest Common Multiple

Articles

Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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3 Jobs Available
Cartographer

How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.

3 Jobs Available
Budget Analyst

Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.

4 Jobs Available
Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Underwriter

An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

3 Jobs Available
Finance Executive
3 Jobs Available
Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
Investment Director

An investment director is a person who helps corporations and individuals manage their finances. They can help them develop a strategy to achieve their goals, including paying off debts and investing in the future. In addition, he or she can help individuals make informed decisions.

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
Plumber

An expert in plumbing is aware of building regulations and safety standards and works to make sure these standards are upheld. Testing pipes for leakage using air pressure and other gauges, and also the ability to construct new pipe systems by cutting, fitting, measuring and threading pipes are some of the other more involved aspects of plumbing. Individuals in the plumber career path are self-employed or work for a small business employing less than ten people, though some might find working for larger entities or the government more desirable.

2 Jobs Available
Construction Manager

Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.

2 Jobs Available
Urban Planner

Urban Planning careers revolve around the idea of developing a plan to use the land optimally, without affecting the environment. Urban planning jobs are offered to those candidates who are skilled in making the right use of land to distribute the growing population, to create various communities. 

Urban planning careers come with the opportunity to make changes to the existing cities and towns. They identify various community needs and make short and long-term plans accordingly.

2 Jobs Available
Highway Engineer

Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

2 Jobs Available
Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems. 

2 Jobs Available
Naval Architect

A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability. 

2 Jobs Available
Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
Veterinary Doctor
5 Jobs Available
Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
Speech Therapist
4 Jobs Available
Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

4 Jobs Available
Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

3 Jobs Available
Hospital Administrator

The hospital Administrator is in charge of organising and supervising the daily operations of medical services and facilities. This organising includes managing of organisation’s staff and its members in service, budgets, service reports, departmental reporting and taking reminders of patient care and services.

2 Jobs Available
Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

4 Jobs Available
Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
Videographer
2 Jobs Available
Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

2 Jobs Available
Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

5 Jobs Available
Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

3 Jobs Available
Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
Linguist

Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning). 

Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian

2 Jobs Available
Public Relation Executive
2 Jobs Available
Travel Journalist

The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
QA Manager
4 Jobs Available
Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Production Manager
3 Jobs Available
Merchandiser
2 Jobs Available
QA Lead

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

2 Jobs Available
Metallurgical Engineer

A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment. 

2 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
QA Manager
4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
ITSM Manager
3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
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