## FACTORS AND MULTIPLES

Factors and Multiples :

Factors are numbers we can multiply together to get a number.

A multiple is the product of a number and any whole number except zero.

To find the factors of a number, we can follow the below steps

Step 1 :

Use multiplication or division facts to find factors. Start with 1 x the given number. Every counting number has at least two factor 1 and the number itself. So, 1 and 8 are factors of 8.

Step 2 :

Test other factor pairs. The only possible whole number factors of 8 are numbers from 1 to 8.

Step 3 :

Continue until the factors repeat

Note :

A factor always divides the product without a remainder.

Question 1 :

Find the factors of 45

Solution : Hence, factors of 45 are 1, 3, 5, 9, 15, 45.

Question 2 :

Write the factors of 15

Solution :

15 = 1 x 15

15 = 5 x 3

Hence, factors of 15 are 1, 3,5 and 15.

Question 3 :

Write the factors of 18

Solution :

18 = 1 x 18

18 = 2 x 9

18 = 3 x 6

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

Question 4 :

List the first 5 multiple of 8

Solution :

To get the first 5 multiple of 8, we need to multiply 8 by 1, 2, 3, 4  and 5 respectively.

1 x 8 = 8

2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

5 x 8 = 40

Hence, first 5 multiple of 8 are 8, 16, 24, 32 and 40.

## How to find how many factors are in a number?

If the given number is small, it is easy to find number of factors.But for larger numbers, we can't just count one by one. This is a nice trick to find how many factors are in an integer.

To find the number of factors of an integer, we need to follow the steps given below.

Step 1 :

Split the given number as prime factors using prime factorization method or tree method.

Step 2 :

Take all exponents and add one to each of them.

Step 3 :

Multiply the modified exponents together.

Let us see an example to understand the above method

Question 5 :

Find the number of factors of 48

Solution :

To get the number of factors of 48, first we have to find the factors.

48 = 1 x 48

48 = 2 x 24

48 = 3 x 16

48 = 4 x 12

48 = 6 x 8

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Number of factors of 48 = 10

We can get the same answer in the below method too.

Step 1 :

For that, first we have to split the given number 48 as prime factors using prime factorization method. Step 2 :

48 = 2⁴ x 3¹

Take all exponents and add one to each of them. So, we get 2 x 3²

Step 3 :

Multiplying the modified exponents, we get 5 x 2 = 10.

Hence, the number of factors of 48 is 10.

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