How to Find All The Factors of a Number (The Factor Pair Method)

Here you shall be using the factor pair method to calculate all the factors of a particular number.

The factor pair method is probably the easiest way to work out all the factors of a particular number. Remember, that a factor divides exactly into a number without a remainder. With your factor pair method, begin with your 1 times tables and see if this goes into your number, then do the 2 times table, then the 3 times table and so on. If you come across a factor that is already found then there will be no more factors to find. Let’s take a look at a couple of question, of using the factor pair method to find factors.

Example 1

Find out all the factors of 16.

Begin with your 1 times table. 16 ÷ 1 is 16. So 1 and 16 are both factors of 16.

After this do your 2 times table. 16 ÷ 2 is 8. So 2 and 8 are both factors of 16.

After this do your 3 times table. 16 ÷ 3 = 5 remainder 1. So 3 is not a factor.

After this do your 4 times table. 16 ÷ 4 is 4. So 4 is a factor of 16.

After this do your 5 times table. 16 ÷ 5 is 3 remainder 1. So 5 is not a factor.

After this do your 6 times table. 16 ÷ 6 is 2 remainder 4. So 6 is not a factor.

After this do your 7 times table. 16 ÷ 7 is 2 remainder 2. So 7 is not a factor.

The next times table is 8, but we already have it as a factor, so there are no more factors to find.

Therefore, all the factors of 16 are:

1,2,4,8,16

Example 2

Find out all the factors of 42.

Begin with your 1 times table. 42 ÷ 1 is 42. So 1 and 42 are both factors of 42.

After this do your 2 times table. 42 ÷ 2 is 21. So 2 and 21 are both factors of 42.

After this do your 3 times table. 42 ÷ 3 is 14. So 3 and 14 are both factors of 42.

After this do your 4 times table. 42 ÷ 4 = 10 remainder 2. So 4 is not a factor.

After this do your 5 times table. 42 ÷ 5 = 8 remainder 2. So 5 is not a factor.

After this do your 6 times table. 42 ÷ 6 is 7. So 6 and 7 are both factors of 42.

The next times table is 7, but we already have it as a factor, so there are no more factors to find.

Therefore, all the factors of 42 are:

1,2,3,6,7,14,21,42.

For some easier questions on using the factor pair method to find factors then click here.

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