Prime Factorisation
Prime factorisation writes a number as a product of prime numbers, and the result is unique for every number.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
Prime factorisation writes a number as a product of prime numbers, and the result is unique for every number.
- Use a factor tree to split a number repeatedly
- 60 equals 2 x 2 x 3 x 5
- Powers shorten repeats, so 60 is 2 squared x 3 x 5
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Prime Factorisation?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Prime Factorisation. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Prime Factorisation in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Prime Factorisation gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Prime Factorisation in detail
Prime factorisation writes a number as a product of prime numbers, such as 60 = 2 × 2 × 3 × 5 or 2² × 3 × 5. You can find it with a factor tree, splitting the number into any factor pair and continuing until every branch ends in a prime, or by dividing repeatedly by the smallest prime possible.
Every integer greater than 1 has exactly one prime factorisation, apart from the order of the factors. This makes it a powerful tool for finding the highest common factor and lowest common multiple, simplifying fractions and working with square roots.
How the interactive helps you understand Prime Factorisation
Click a step, or use the Previous and Next buttons, to move through the sequence one stage at a time. Auto-play moves on for you.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Prime Factorisation.
Real-life uses and examples
- Explain Prime Factorisation to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Prime Factorisation in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Prime Factorisation by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Prime Factorisation without checking why they work.
- Forgetting units, signs or brackets when you apply Prime Factorisation.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Prime Factorisation
What is Prime Factorisation?
Prime factorisation writes a number as a product of prime numbers, and the result is unique for every number.
What are the most important points about Prime Factorisation?
The main points are: Use a factor tree to split a number repeatedly; 60 equals 2 x 2 x 3 x 5; Powers shorten repeats, so 60 is 2 squared x 3 x 5.
Why is Prime Factorisation useful?
Understanding Prime Factorisation gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Prime Factorisation?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Prime Factorisation?
Related topics in Mathematics include Divisibility Rules, Fractions, Multiplying and Dividing Fractions.