# Multiples and Factors

## Multiples

The multiples of a number are the values in that number’s times table. For example, the multiples of 5 are 5, 10, 15, 20, 25 and so on.

There are an amount of multiples of any given number.

## Factors

A factor is an that will divide exactly into another number. For example, 8 is a factor of 24 because 8 will divide into 24 exactly 3 times with no remainder.

## Factor pairs

Factor pairs are two integers which multiply together to make a particular number. For example, the factor pairs of 12 are 1 and 12; 2 and 6; 3 and 4. This means that the factors of 12 (in order) are 1, 2, 3, 4, 6 and 12. Writing factors in pairs helps to avoid missing any out.

### Example

List all the factors of 24.

The smallest integer that will divide exactly into 24 is 1. Remember, 1 is a factor of every whole number. 1 will divide into 24 exactly 24 times (because ) so 24 is the factor pair that fits with 1.

Once the first factor pair has been recorded, move onto the next integer, 2. Consider whether this will divide into 24 or not. 2 will divide into 24 exactly 12 times, so 2 and 12 are factor pairs.

Considering each integer in turn and whether it will divide into 24 or not. If so, write it as a factor pair in the list.

All factor pairs will have been found when the next integer to consider is already in the list.

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.