What is a factor?
Year 5 finds all the factor pairs of a number and the common factors of two numbers. Year 6 uses common factors to simplify fractions. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
A factor is a whole number that divides into another number exactly, with nothing left over.
What it means
4 is a factor of 12, because 12 ÷ 4 = 3 exactly. 5 is not a factor of 12, because 12 ÷ 5 leaves a remainder.
Factors come in pairs that multiply to make the number: 1 × 12, 2 × 6 and 3 × 4. So the factors of 12 are 1, 2, 3, 4, 6 and 12.
A common factor of two numbers is a factor of both of them. The biggest one is called the highest common factor.
A worked example
Find all the factors of 18
- Start at 1 and look for pairs: 1 × 18, 2 × 9, 3 × 6.
- 4 and 5 do not go into 18. The next one, 6, is already in a pair, so stop.
- The factors of 18 are 1, 2, 3, 6, 9 and 18.
The common mistake
Mixing up factors and multiples. The factors of 12 are the numbers that fit into 12, so none is bigger than 12. The multiples of 12 (12, 24, 36 and so on) come out of the 12 times table.
How it comes up in the 11+
What is the highest common factor of 24 and 36?
Answer: 12
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Common factors: 1, 2, 3, 4, 6, 12. The highest is 12.
Related words and practice
More maths words
Questions parents ask
Is 1 a factor of every number?
Yes. Every whole number can be divided by 1 exactly, so 1 is always a factor.
Is a number a factor of itself?
Yes. 12 ÷ 12 = 1 exactly, so 12 is a factor of 12. Every number bigger than 1 has at least two factors: 1 and itself.
Knowing the words is half of an 11+ maths question
11+ papers use maths vocabulary without explaining it. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.