How Many Multiples of 4 Lie Between 10 and 205

You all might have heard about the term multiple and factor and also got confused between these two terms. Here I am telling you what is multiple and what is a factor in simple terms. To find the multiple of any number we need to multiply it. Whereas a factor is any number which divides the given number exactly. Now, here we have to Calculate how many multiples of 4 lie between 10 and 205. 49 multiples of 4 are lying between 10 and 205. To find this we have to use arithmetic progression. What is arithmetic progression (A. P)? Let's learn what A. P is before knowing the proper solution to our question.

What are Multiples?

A multiple is a number which can be obtained by multiplying a number with an integer or it can also be defined as a product of an integer and a particular quantity. Some of the multiples of 4 lying between 10 and 205 are 12,16,20,24,28….

The last multiple of 4 is 204 which is lying between 10 and 205.

What is An A.P?

A.P. can be defined as a sequence of numbers having a common difference between two consecutive numbers or terms. For example 2,4,6,8… make an A.P. here the common difference is 2.

The general form of A.P is a1, a2, a3…

And d represents a common difference which can be obtained by subtracting two consecutive terms.

The most commonly used formula for the general term of A.P. is

an= a+(n-1)d.

Where an is the last term, a is the first term, n is the number of terms and d is a common difference.

Multiples of 4 Lie Between 10 and 205.

Here we can use Arithmetic progression to find multiples between 10 and 205. So, here the first term after 10 which is divisible by 4 is 12 and the last term which is divisible by 4 is 204.

So, 12,16,20,24….. 204 make an A.P.

We can use the above formula i.e

an=a+(n-1)d.

Here a = 12,

d= 16-12 = 4

an= 204

we have to find n

Using above formula

204= 12+(n-1)×4

192 = (n-1)×4

192/4 =(n-1)

48=(n-1)

n=49.

So, 49 is the number of terms.

Hence there are 49 multiples between 10 and 205.

Let's try some more examples:

• How many multiples of 4 lie between 101 and 205?

Now again this can be solved with the help of A. P.

First term = a = 104

Last term = an = 204

Common difference = d = 4

an = a + (n-1)d

204 = 104 + (n-1)4

100/4 = n-1

25 = n-1

n = 26.

26 multiples of 4 lie between 101 and 205.

• How many multiples of 4 lie between 201 and 301?

Use A. P to solve this problem.

First term = a = 204

Last term = an = 300

common difference = d = 4

an = a + (n-1)d

300 = 204 + (n-1)4

96 = (n-1)4

96/4 = (n-1)

24 = (n-1)

n = 25.

25 multiples of 4 lie between 201 and 301.

• How many multiples of 4 lie between 51 and 98?

Use A. P to solve this problem.

First term = a = 52

Last term = an = 96

Common difference= d = 4

an = a + (n-1)d

96 = 52 + (n-1)4

44 = (n-1)4

44/4 = (n-1)

11 = n-1

n = 12.

12 multiples of 4 lie between 51 and 98.