Operations and Algebraic Thinking
Factor pairs and multiples
Find the factor pairs of a number, list its multiples, and spot factors and multiples two numbers share.
A factor of a number divides into it exactly, with nothing left over. A multiple is what you get by multiplying a number by 1, 2, 3 and onwards. The two words describe the same fact from opposite ends: 3 is a factor of 12, and 12 is a multiple of 3.
Factors come in pairs
Every factor has a partner it multiplies with to make the number. 24 is 1 × 24, 2 × 12, 3 × 8 and 4 × 6 — so finding one factor always hands you a second one free.
Worked example
Is 6 a factor of 30?
Ask whether 30 can be split into equal groups of 6.
That is what being a factor means — equal groups, nothing left over.
Try it together
Let us find every factor of 24 together, in pairs.
Work upwards from 1 and write down both halves of each pair. You can stop as soon as the pairs start repeating themselves.
1.Start at 1. What must 1 be multiplied by to reach 24?
Have a go
Have a go on your own: what is the partner of 5 in a factor pair of 35?
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.