Factors, multiples and primes · Grade 8

In Grade 8 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

Example 1

Write 60 as a product of prime factors.

Answer: 2^2 × 3 × 5

Example 2

Find the HCF and LCM of 24 and 36.

Answer: HCF 12, LCM 72

Example 3

Two lighthouses flash every 8 seconds and every 12 seconds. They flash together now. When do they next flash together?

Answer: After 24 seconds

Other years