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.

2 times 5 equals 10 If we multiply 1 and 10 together, the answer is 10. 1 and 10 are also factors of 10.

1 times 10 equals 10 The factors of 10 are:

1, 2, 5 and 10 are factors of 10

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 = 6

    The factors of 6 are:

    1, 2, 3 and 6 are the factors of 6
  • The factors of 18 are the numbers that multiply together to make 18.

    1 × 18 = 18

    2 × 9 = 18

    3 × 6 = 18

    The factors of 18 are:

    1, 2, 3, 6, 9 and 18 are factors of 18
  • 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 = 48

    The factors of 48 are:

    1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 are the factors of 48

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