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.

Example 1 :

Find the factors of 45.

Solution :

Factors of 45 are 1, 3, 5, 9, 15, 45. 

Example 2 :

Write the factors of 15.

Solution :

15  =  1 x 15

15  =  5 x 3

Factors of 15 are 1, 3,5 and 15.

Example 3 :

Write the factors of 18.

Solution :

18  =  1 x 18

18  =  2 x 9

18  =  3 x 6

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

Example 4 :

List the first 5 multiples 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

First 5 multiples of 8 are 8, 16, 24, 32 and 40.

Number of Factors of 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

Example 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 2⁵ 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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