Factors and Multiples
Factors divide a number exactly while multiples are its times table.
About this topic
Factors are numbers that divide another number exactly, with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12. Multiples go the other way: they are what you get by multiplying a number by 1, 2, 3 and so on, giving a times table.
Every number is both a factor and a multiple of itself, and 1 is a factor of everything. To find all factors, test whole numbers in order and record them in pairs: for 36 you get 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 on its own, since 6 × 6 = 36. You only need to test up to the square root. A number is a perfect square when it has an odd number of factors.
Suppose two buses leave a station together, one every 6 minutes and one every 8 minutes. They leave together again at a common multiple, and the first time is the least one, 24 minutes. Meanwhile, factors help when arranging 24 chairs in equal rows: 1, 2, 3, 4, 6, 8, 12 or 24 chairs per row all work.
Factors and multiples underpin fractions, ratios, common denominators and problems about repeating cycles. Students often mix up the two words. A handy memory trick is that factors are few and are never bigger than the number, while multiples go on forever and are never smaller than it.
Key ideas
- Factors of 12 are 1, 2, 3, 4, 6 and 12
- Multiples of 4 are 4, 8, 12, 16 and so on
- Every number is a factor and multiple of itself
Quick check
Use cases: where Factors and Multiples helps
- Homework: review the key idea behind Factors and Multiples before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Factors and Multiples without notes.
- Visual learning: play with the interactive lab to see how Factors and Multiples changes when you adjust its inputs.
- Teaching a friend: explain Factors and Multiples in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Factors and Multiples?
Factors divide a number exactly while multiples are its times table.
What will I learn in Factors and Multiples?
Factors of 12 are 1, 2, 3, 4, 6 and 12. Multiples of 4 are 4, 8, 12, 16 and so on. Every number is a factor and multiple of itself.
Is Factors and Multiples part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Factors and Multiples lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Factors and Multiples?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.