Factors, multiples and primes

Factors divide into a number exactly; multiples are in its times table. A prime has exactly two factors: 1 and itself. Every whole number can be written as a product of primes, which helps find the highest common factor (HCF) and lowest common multiple (LCM).

Key facts

  • Factors of 12: 1, 2, 3, 4, 6, 12.
  • Multiples of 12: 12, 24, 36, 48…
  • 1 is not prime. 2 is the only even prime.
  • HCF: the biggest factor two numbers share. LCM: the smallest multiple they share.

Worked examples

Example 1

Write 60 as a product of prime factors.

  1. Split 60 into two factors. 60 = 6 × 10
  2. Keep splitting until every branch is prime. 6 = 2 × 3, 10 = 2 × 5
  3. Collect the primes. 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5

Answer: 2² × 3 × 5

Example 2

Find the HCF and LCM of 18 and 24.

  1. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. HCF = 6
  2. Multiples of 24: 24, 48, 72. 72 is also a multiple of 18. LCM = 72

Answer: HCF 6, LCM 72