Factors, multiples and primes · Year 9

In Year 9 you get fluent with: HCF and LCM from prime factors.

Factors are numbers that divide exactly into a number; multiples are the numbers in its times table. Primes, which have exactly two factors, are the building blocks: every whole number can be written as a product of primes in just one way. HCF and LCM solve real problems about sharing and timing.

Key facts

• A factor of 12 divides into it exactly: 1, 2, 3, 4, 6, 12. Find factors in pairs.
• Multiples of 7: 7, 14, 21, 28, … (they go on for ever).
• Product of primes: use a factor tree, e.g. 60 = 2^2 × 3 × 5.
• HCF (highest common factor): the biggest number that divides both. Use it for 'cut into equal pieces' questions.
• LCM (lowest common multiple): the smallest number in both times tables. Use it for 'when together again' questions.
• Divisibility: by 3 if the digits add to a multiple of 3; by 4 if the last two digits are a multiple of 4.

Worked examples

Other years

• Factors, multiples and primes · Year 4
• Factors, multiples and primes · Year 5
• Factors, multiples and primes · Year 6
• Factors, multiples and primes · Year 7
• Factors, multiples and primes · Year 8