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Factors
(KS2, Year 4)
The Lesson
A factor is a number which divides exactly into another number. The numbers that are multiplied together to make another number are factors.Dictionary Definition
The Oxford English Dictionary defines a factor as "each of two or more whole numbers or quantities which, when multiplied together, produce a given number or expression."A Real Example of Factors
It is easier to understand factors with an example. If we multiply 2 and 5 together, the answer is 10. 2 and 5 are factors of 10.If we multiply 1 and 10 together, the answer is 10. 1 and 10 are also factors of 10.
The factors of 10 are:
Dividing by Factors
We have seen that 1,2, 5 and 10 are factors of 10. All of these numbers divide exactly into 10:
10 ÷ 1 = 10
10 ÷ 2 = 5
10 ÷ 5 = 2
10 ÷ 10 = 1
Note: When we divide a number by one of its factors, the answer is another factor.
More Real Examples of Factors

The factors of 6 are the numbers that multiply together to make 6.
1 × 6 = 6 2 × 3 = 6The factors of 6 are:

The factors of 18 are the numbers that multiply together to make 18.
1 × 18 = 18 2 × 9 = 18 3 × 6 = 18The factors of 18 are:

The factors of 48 are the numbers that multiply together to make 48.
1 × 48 = 48 2 × 24 = 48 3 × 16 = 48 4 × 12 = 48 6 × 8 = 48The factors of 48 are:
Factor, Factorisation
To write a number or term as a product of its factors is called 'to factor' or 'to factorise'. For example, to factor (or factorise) 10, we can write:
1 × 10 = 10
2 × 5 = 10
The method is refered to as 'factoring' or 'factorising'.
Factors, Prime and Composite Numbers
 If the only factors of a number are 1 and itself, then the number is a prime number. For example, 5 is a prime number because its only factors are 1 and 5.
 If a number has at least one factor other than 1 and itself, it is a composite number. For example, 6 is a composite number as its factors are 1, 2, 3 and 6.
Factors in Algebra
Just as numbers have factors, terms in algebra also have factors. A factor is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term. For example, the factors of 2 and x are factors of 2x, because 2 × x = 2x. Read more about factors in algebra Do you disagree with something on this page?
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