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NCERT solutions for class 10 maths chapter 1 exercise 1.2 are discussed here that particularly deals with Fundamental Theorem of Arithmetic. The NCERT solutions for class 10 maths ex 1.2 include seven questions which are easy-to-solve questions that also cover the basics of HCF and LCM, Real Numbers, factorization, the prime numbers, real numbers, and many more.
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NCERT solutions for exercises are created by expert team at Careers360 considering the latest syllabus and pattern of CBSE 2023-24, covering step by step, comprehensive solutions of every problem. Students can find list of exercised below and practice problems to command the concepts.
Real Numbers Class 10 Chapter 1 - Exercise 1.2
Q1 (1) Express each number as a product of its prime factors: 140
Answer:
The number can be as a product of its prime factors as follows
Q 1 (2) Express each number as a product of its prime factors: 156
Answer:
The given number can be expressed as follows
Q1 (3) Express each number as a product of its prime factors: 3825
Answer:
The number is expressed as the product of the prime factors as follows
Q1 (4) Express each number as a product of its prime factors: 5005
Answer:
The given number can be expressed as the product of its prime factors as follows.
Q1 (5) Express each number as a product of its prime factors: 7429
Answer:
The given number can be expressed as the product of their prime factors as follows
Answer:
26 = 2 x 13
91 = 7 x 13
HCF(26,91) = 13
LCM(26,91) = 2 x 7 x 13 = 182
HCF x LCM = 13 x 182 = 2366
26 x 91 = 2366
26 x 91 = HCF x LCM
Hence Verified
Answer:
The number can be expressed as the product of prime factors as
510 = 2 x 3 x 5 x 17
92 = 2 2 x 23
HCF(510,92) = 2
LCM(510,92) = 2 2 x 3 x 5 x 17 x 23 = 23460
HCF x LCM = 2 x 23460 = 46920
510 x 92 = 46920
510 x 92 = HCF x LCM
Hence Verified
Answer:
336 is expressed as the product of its prime factor as
336 = 2 4 x 3 x 7
54 is expressed as the product of its prime factor as
54 = 2 x 3 3
HCF(336,54) = 2 x 3 = 6
LCM(336,54) = 2 4 x 3 3 x 7 = 3024
HCF x LCM = 6 x 3024 = 18144
336 x 54 = 18144
336 x 54 = HCF x LCM
Hence Verified
Answer:
The numbers can be written as the product of their prime factors as follows
12 = 2 2 x 3
15 = 3 x 5
21 = 3 x 7
HCF = 3
LCM = 2 2 x 3 x 5 x 7 = 420
Answer:
The given numbers are written as the product of their prime factors as follows
17 = 1 x 17
23 = 1 x 23
29 = 1 x 29
HCF = 1
LCM = 17 x 23 x 29 = 11339
Answer:
The given numbers are written as the product of their prime factors as follows
8 = 2 3
9 = 3 2
25 = 5 2
HCF = 1
LCM = 2 3 x 3 2 x 5 2 = 1800
Q4 Given that HCF (306, 657) = 9, find LCM (306, 657).
Answer:
As we know the product of HCF and LCM of two numbers is equal to the product of the two numbers we have
HCF (306, 657) x LCM (306, 657) = 306 x 657
Q5 Check whether can end with the digit 0 for any natural number n.
Answer:
By prime factorizing we have
6 n = 2 n x 3 n
A number will end with 0 if it has at least 1 as the power of both 2 and 5 in its prime factorization. Since the power of 5 is 0 in the prime factorization of 6 n we can conclude that for no value of n 6 n will end with the digit 0.
Q6 Explain why 7 11 13 + 13 and 7 6 5 4 3 2 1 + 5 are composite numbers.
Answer:
7 x 11 x 13 + 13
= (7 x 11 + 1) x 13
= 78 x 13
= 2 x 3 x 13 2
7 x 6 x 5 x 4 x 3 x 2 x 1 + 5
= (7 x 6 x 4 x 3 x 2 x 1 + 1) x 5
= 5 x 1008
After Solving we observed that both the number are even numbers and the number rule says that we can take atleast two common out of two numbers. So that the number is composite number.
Answer:
The time after which they meet again at the starting point will be equal to the LCM of the times they individually take to complete one round.
Time taken by Sonia = 18 = 2 x 3 2
Time taken by Ravi = 12 = 2 2 x 3
LCM(18,12) = 2 2 x 3 2 = 36
Therefore they would again meet at the starting point after 36 minutes.
This Exercise 1.2 Class 10 Maths gives questions on the factorization of composite numbers. Composite numbers are numbers that have more than two factors. Mathematically, the natural numbers which are not prime numbers come under composite numbers as they can be divided by more than two numbers. This class 10 maths ex 1.2 mainly focused on the concepts of HCF and LCM. Except this ex 1.2 class 10 solutions students can also refer Real Numbers Class 10 Notes to command the concepts in detail.
Also see-
Zero is neither prime nor a composite number because it does not have any prime factors.
The prime factors of 144,
144 = 2 × 2 × 2 × 2 × 3 × 3
Students can practice problems discussed in class 10 ex 1.2 to command these concepts.
The full form of HCF is “Highest Common Factor” and LCM is “Least common multiple”.
The methods used in finding LCM and HCF are the prime factorization method and long division method.
104 = 2 × 2 × 2 × 13
160 = 2 × 2 × 2 × 2 × 2 × 5
The common factors of 104 and 160 are 2 × 2 × 2 = 8
Therefore, HCF (104, 160) = 8
21=3×7
28=4×7
Now, LCM (21, 28)=7×4×3=84
The formula that involves both HCF and LCM is
(HCF of the two numbers) x (LCM of the two numbers)= Product of Two numbers
Let the other number be a.
We know that,
(HCF of the two numbers) x (LCM of the two numbers)= Product of Two numbers
Now, 7×84=21×a
588=21a
Which on dividing both sides by 21 ,
We get, a=28
The other number is 28 .
Theorem: Every composite number may be factored as a product of primes, which means that any composite number can be expressed as a product of primes
The questions are based on the concept of the Fundamental Theorem of Arithmetic, in finding HCF and LCM, questions related to the relationship of HCF and LCM.
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Thanking you
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