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What is a factor?

A factor is a whole number that divides exactly into another number without a remainder. For example:

15 ÷ 3 = 5, so 3 is a factor of 15.

1, 5 and 15 are also factors of 15.


What is a factor pair?

A factor pair is a set of two whole numbers that give a particular product when multiplied together. For example:

3 x 5 = 15, so 3 and 5 are a factor pair for the product of 15.

3 and 5 also divide exactly into 15 without any remainders.

15 has one other factor pair: 1 and 15.


Example: Factors of 24

A table to show Factors and Factors Pairs of 24

What is a prime factor?

A prime factor is a factor that is also a prime number. It can only be divided by 1 and by itself.


What is a factor tree?

A factor tree is a way of expressing the factors of a number, specifically the prime factors. Each branch is split into factors. Once the factor at the end of a branch is a prime number, that branch stops.

A Factor Tree showing the prime factors of 24
A Factor Tree showing the prime factors of 24
A Factor Tree showing the prime factors of 24

There are several different ways to begin the branches, but they will all eventually lead to the same prime factors.

The prime factors of 24 are 2 and 3.


What are common factors?

A common factor is a whole number which is a factor of two or more numbers. For example:

A table to show Common Factors of 16 and 24

1 is a common factor of all whole numbers.

LESSON: Factor Pairs | Year 4

LESSON PACK Factors and Multiples | Year 5

LESSON PACK Factors, Multiples and Primes | Year 6

FREE Factor Pairs Worksheet