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
- Build factor pairs with arrays: 12 counters can make a 1×12, 2×6 or 3×4 rectangle, each rectangle is a factor pair.
- List factors systematically in pairs from the outside in (1 and 12, 2 and 6, 3 and 4) so none get missed.
- Contrast the words directly: factors of 12 are 12 or smaller and run out; multiples of 12 are 12 or bigger and never end.
- Play fizz-buzz style games for multiples; use divisibility checks (even numbers, digit sums for 3) for factors.
- 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).
Frequently asked questions
What is the difference between a factor and a multiple?
A factor divides a number exactly, so 1, 2, 3, 4, 6 and 12 are factors of 12. A multiple is the result of multiplying, so 12, 24 and 36 are multiples of 12. Factors of a number are that number or smaller and run out; its multiples are that number or bigger and never end.
What age or grade are factors and multiples taught?
Factors and multiples are usually taught from Grade 4 to Grade 6, once multiplication is fluent. They underpin fractions, prime numbers, and greatest common factor and lowest common multiple work, so a secure grasp here supports much of upper-primary number work.
How do you find all the factors of a number?
List them in pairs from the outside in. For 12, start with 1 and 12, then 2 and 6, then 3 and 4. Working through the pairs in order means none get missed. When the pairs meet or overlap, you have found them all.
Does a bigger number have more factors?
Not necessarily. The number of factors depends on structure, not size. For example 60 has twelve factors while 61, a prime, has only two. So a large number can have fewer factors than a smaller one, which surprises many students.
Why does my child mix up factors and multiples?
The two words point in opposite directions of the same fact family, so they are easily swapped, with children listing 24 and 36 as 'factors' of 12. Contrasting them directly, factors run down and stop while multiples run up forever, keeps the two ideas apart.
How do factors relate to prime numbers?
A prime number has exactly two factors, 1 and itself, so it cannot be split into smaller equal groups. A composite number has more than two factors. Listing the factors of a number and counting them is the direct way to decide whether it is prime.
Are 1 and the number itself always factors?
Yes. Every whole number has 1 and itself as factors, because 1 times the number equals the number. Children often forget to include these two, so it is worth stressing that they always belong in the list.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.