Factors

Factors are numbers that divide into another number exactly.

The factors of 4 are 1, 2 and 4.

1 because 4 ÷ 1 = 4

2 because 4÷ 2 = 2

4 because 4÷ 4 = 1

Four doesn’t have any other factors.

The factors of 6 are 1, 2, 3 and 6

Let’s find all the factors of 36

One and the number itself are always factors. So, 1 and 36 are factors of 36.

36 ÷ 2 = 18. This means that 2 and 18 are both factors of 36 because 36 ÷ 2 = 18 means that 36 ÷ 18 = 2.

36 ÷ 3 = 12

36 ÷ 4 = 9

36 doesn’t divide by 5 to leave a whole number

36 ÷ 6 = 6

We know we can stop looking now because if we divide 36 by any number higher than 6 then the result will be less than 6 and we have already found all the factors of 36 that are 6 or below.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36

Another way to define factors is one or more numbers multiplied together to produce a given number

18 and 2 are factors 0f 36, for example, because they can be multiplied together to produce 36.

Factors are commonly spoken about in this way: Four is a factor of thirty six because four \times nine equals thirty six. The product of three and twelve is thirty six so three and twelve are factors of thirty six.