Factor pairs come in matching pairs
If 4 x 9 = 36, then 4 and 9 are a factor pair of 36.
factor pair
factor pair
factor pair
Stop when the pairs begin to repeat in the opposite order.
Year 7
Prime factorisation and factor pairs
Recognise prime numbers, find factor pairs efficiently, and write composite numbers as products of prime factors.
Lesson overview
Number - factors, multiples and primes
Factors tell us how a number can be built through multiplication. A prime number has exactly two factors, 1 and itself. Composite numbers can be split into factor pairs and then broken down again until every factor is prime. This helps us see structure clearly and prepares us for later work with fractions, algebra and ratio.
Prime numbers only have two factors
A prime number is divisible by 1 and itself, but no other whole numbers.
| Number | Prime or composite | Reason |
|---|---|---|
| 29 | Prime | only 1 and 29 |
| 21 | Composite | 3 x 7 |
| 39 | Composite | 3 x 13 |
Test divisibility by small primes such as 2, 3 and 5 first.
Prime factorisation breaks a number into prime pieces
24 can be split into 6 x 4, then 6 = 2 x 3 and 4 = 2 x 2.
A prime factorisation is complete only when every factor is prime.
Worked example
Write 60 as a product of prime factors.
- Choose a factor pair of 60, such as 6 x 10.
- Split 6 into 2 x 3 because both are prime.
- Split 10 into 2 x 5 because both are prime.
- So 60 = 2 x 2 x 3 x 5.
Try it
Look for factor pairs first, then keep splitting until all factors are prime.
Question 1
Which pair is a factor pair of 36?
Question 2
Which number is prime?
3 x 7
test factors
3 x 13
Question 3
What is the prime factorisation of 24?
Question 4
Which statement is true?
Question 5
How do you know 21 is composite?
| Number | Known factors |
|---|---|
| 21 | 1, 3, 7, 21 |
Common mistakes
Watch for these when working through the lesson.
- Calling 1 a prime number even though it has only one factor.
- Stopping a factorisation too early with a composite number still showing.
- Missing a factor pair because the search was not systematic.
Related topics
These ideas fit closely with this lesson.
- Mental and written arithmetic with integers, decimals and fractions.
- Operations with negative numbers.
- Simplify linear expressions.