Prime numbers, factors and multiples are essential building blocks for a lot of number work. Knowledge of how to use these numbers will improve arithmetic and make calculations more efficient.

A multiple of a number is any integer multiplied by the number. For example, 15 is a multiple of 5 because

Listing multiples of 5 gives 5, 10, 15, 20, 25 and so on

There are an infinite amount of multiples of any given number.

Factors

A factor is an integer (whole number) 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 numbers 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 out any numbers.

Example

List all the factors of 24.

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

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

Keep considering each number 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 number to consider is already in the list.

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