Foundation and Higher · factors and multiples

Factors or
multiples? Never
mix them up.

factors fit in,
multiples grow

two words that get swapped —

Factors

divide into a number exactly

multiples are its times table

step 1 of 4

List factors in pairs

1. Start at 1 and work up in pairs.

2. 5 does not go. Stop when the pairs meet.

✓ All 8 factors, none missed

factors of 24

1 × 24 2 × 12

3 × 8 4 × 6

1, 2, 3, 4, 6, 8, 12, 24

step 2 of 4

Multiples keep going

1. Multiples are the times table.

2. The first multiple is the number itself.

✓ Factors end. Multiples never do.

multiples of 6

6, 12, 18, 24, 30, …

6 × 1, 6 × 2, 6 × 3, …

step 3 of 4

Primes: two factors

1. A prime has exactly two factors.

2. 1 has only one factor: not prime.

✓ Learn the primes up to 20

2, 3, 5, 7, 11, 13, 17, 19

7 = 1 × 7 and nothing else

1 is not prime

2 is the only even prime

step 4 of 4

Common ones

1. HCF: biggest factor in both lists.

2. LCM: first multiple in both lists.

✓ HCF is small, LCM is big

12:  1, 2, 3, 4, 6, 12

18:  1, 2, 3, 6, 9, 18

HCF = 6

12, 24, 36 … 18, 36 …

LCM = 36

factors, multiples, primes —

Factors

divide in exactly: list in pairs

Multiples

the times table: never ends

Primes

exactly two factors

Big numbers? Use prime
factor trees instead.

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