Factors and Multiples
A factor divides a number exactly, and a multiple is the result of multiplying that number by a whole number.
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Play with the controls to see the idea in action.
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A factor divides a number exactly, and a multiple is the result of multiplying that number by a whole number.
- Factors of 12 are 1, 2, 3, 4, 6 and 12
- Multiples of 4 are 4, 8, 12, 16 and so on
- A number is always a factor and a multiple of itself
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Factors and Multiples?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Factors and Multiples. 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 Factors and Multiples in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Factors and Multiples gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Factors and Multiples in detail
A factor of a number divides it exactly with no remainder, so the factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is what you get by multiplying the number by a whole number, so the multiples of 4 are 4, 8, 12, 16 and so on. Factors and multiples are two sides of the same relationship.
These ideas underpin simplifying fractions, finding common denominators, solving timetable or pattern problems and, later, factorising algebra. Listing factors in pairs (1 × 12, 2 × 6, 3 × 4) is a reliable way to make sure none are missed.
How the interactive helps you understand Factors and Multiples
Click a card to flip it and reveal the answer, then move on to the next one.
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 Factors and Multiples.
Real-life uses and examples
- Check a homework answer about Factors and Multiples by estimating first, then working it out step by step.
- Use Factors and Multiples when comparing prices, discounts or recipe quantities in everyday life.
- Explain Factors and Multiples to a friend with a simple picture, such as a row of tiles or a bag of sweets.
Common mistakes to avoid
- Memorising the steps for Factors and Multiples without checking why they work.
- Forgetting units, signs or brackets when you apply Factors and Multiples.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Factors and Multiples
What is Factors and Multiples?
A factor divides a number exactly, and a multiple is the result of multiplying that number by a whole number.
What are the most important points about Factors and Multiples?
The main points are: Factors of 12 are 1, 2, 3, 4, 6 and 12; Multiples of 4 are 4, 8, 12, 16 and so on; A number is always a factor and a multiple of itself.
Why is Factors and Multiples useful?
Understanding Factors and Multiples gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Factors and Multiples?
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 Factors and Multiples?
Related topics in Mathematics include Highest Common Factor, Order of Operations, Equivalent Fractions.