How to teach factors and multiples

Grade 4 to Grade 6

A factor divides a number exactly: 1, 2, 3, 4, 6 and 12 are the factors of 12. A multiple is the result of multiplying: 12, 24, 36 are multiples of 12. The two words are opposite directions of the same fact family, and they underpin fractions, primes and algebra.

How to teach it

1. Build factor pairs with arrays: 12 counters can make a 1×12, 2×6 or 3×4 rectangle , each rectangle is a factor pair.
2. List factors systematically in pairs from the outside in (1 and 12, 2 and 6, 3 and 4) so none get missed.
3. Contrast the words directly: factors of 12 are 12 or smaller and run out; multiples of 12 are 12 or bigger and never end.
4. Play fizz-buzz style games for multiples; use divisibility checks (even numbers, digit sums for 3) for factors.
5. Link to primes: a prime has exactly two factors, 1 and itself.

Common mistakes

• Mixing up the words , listing 24, 36 as 'factors' of 12.
• Missing factor pairs by listing randomly instead of in order.
• Forgetting 1 and the number itself are always factors.
• Thinking a number with many factors must be big (60 has more factors than 61).