### What is a factor?

The definition of factor is a number that fits exactly into a given number, or divides a particular number with no remainder (fraction or decimal). They can also be identified as pairs of numbers that multiply together to make another number. A factor is always a positive integer (whole number).

### What are factors of a number?

Factors are divisors (they can be positive or negative numbers) of a given whole number. A number may have many factors, possible factors can be found using a factor tree or divisibility rules.

Examples of factors in maths

5 is a factor of 10, 15, 20, 25, etc. because 10 ÷ 5 = 2, 15 ÷ 5 = 3, 20 ÷ 5 = 4, 25 ÷ 5 = 5, etc.; therefore, all the numbers in the 5 times table have 5 as a factor. When finding factors, it’s useful to look for them in pairs as two factors will multiply to make another number. The factor pairs of 12 are 1 x 12, 2 x 6 and 3 x 4, so the factors of 12 are 1, 2, 3, 4, 6 and 12.

Square numbers have an odd number of factors as one of the factors is multiplied by itself – for example, the factor pairs of 25 are 1 x 25 and 5 x 5, so the factors of 25 are 1, 5 and 25.

Prime numbers only have two factors – themselves and 1.