What Are Factors: Explained for Primary School
Factors start to be mentioned in primary school from about Year 4. Here you’ll find out what children will be taught and need to know about factors. A secure knowledge of times tables is essential in understanding factors.
What is a factor?
A 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).
Note: Children often confuse factors with multiples.
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.
Examples of factors in maths
5 is a factor of 10, 15, 20, 25, etc. because 10 ÷ 5 = 2, 15 ÷ 3 = 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.
When do children learn about factors in the national curriculum?
Pupils will first encounter factors in Year 4, where they will:
- recognise and use factor pairs and commutativity in mental calculations
- use factors and multiples to recognise equivalent fractions and simplify where appropriate
In Year 5, children will:
- identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
- know and use the vocabulary of prime numbers, prime factors and composite numbers
- solve problems involving multiplication and division including using their knowledge of factors and multiples, square numbers and cube numbers
And finally in Year 6, where children will be expected to:
- identify common factors, common multiples and prime numbers
- use common factors to simplify fractions
Factors, Multiples, Square & Cube Numbers Pack
Download a free factors, multiples, square and cube numbers pack to help your class learn about factors.
What is the highest common factor?
The highest common factor (or greatest common factor) is the largest factor shared between two given numbers. For example, the highest common factor of 12 and 16 is 4 as it is the largest number that both given numbers can be divided by without remainders. Highest common factors can be used to simplify fractions.
Read more: What is the Highest Common Factor?
How do factors relate to other areas of maths?
Common factors are used when simplifying fractions. Factors are also useful when discussing the area of a rectangle or volume of a cuboid.
Factors in real life
Prime factors are often used in cyber security, to encrypt information.
Factors are also useful when organising a number into groups – for example, a class of 28 children could be split into 2 groups of 14, 4 groups of 7, 7 groups of 4 or 14 groups of 2.
6 factor practice questions and answers
- The factors of a number are 1, 2, 3, 5, 6, 10, 15 and 30. What is the number?
- List the factors of 24.
- What’s the highest common factor of 24 and 30?
- Write three factors of 30 that are not factors of 15. (SATs 2017)
- Tick the numbers that are common factors of both 12 and 18: 2, 3, 6, 9, 12 (SATs 2018)
- Here are five numbers: 2 3 4 5 6. Write each number on the correct cards. The number 2 has been written on the correct cards for you. (SATs 2019)
- 1, 2, 3, 4, 6, 8, 12, 24
- 2, 6, 30
- 2, 3, 6
- Prime numbers: 2, 3, 5
Factors of 12: 2, 3, 4, 6
Factors of 15: 3, 5
The factors of 12 are 1, 2, 3, 4, 6 and 12.
The factors of 21 are 1, 3, and 7.
An easy way to explain factors to children is that “factors are friends – they come in pairs”. Using a “factor rainbow” or “factor spider” are good ways of visualising these pairs.
For guides on introducing more new words in primary maths, take a look at our primary maths dictionary
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