GCSE Mathematics (9-1)

2.2 Prime factorisation, HCF and LCM — Practise with help

Try each question first. Open a hint if needed, then check the full working.

Warm-up: remember

  1. Is 13 prime? State its factors.
  2. Find two factors shared by 18 and 30.
Answers
  1. Yes; 1 and 13.
  2. For example, 1 and 6.

Practise with help

1. Write 48 as a product of prime factors.

Hint

Divide by 2 while the result is even.

Next step

48=2×24=2×2×12=2×2×2×648=2\times24=2\times2\times12=2\times2\times2\times6.

Full working

48=2×2×2×2×3=24×348=2\times2\times2\times2\times3=2^4\times3.

2. Find the HCF of 18 and 30.

Hint

Write each number as prime factors and take shared primes with smaller powers.

Next step

18=2×3218=2\times3^2 and 30=2×3×530=2\times3\times5.

Full working

The shared factors are 2×3=62\times3=6, so the HCF is 6.

3. Find the LCM of 8 and 12.

Hint

Use each prime with its greater power.

Next step

8=238=2^3 and 12=22×312=2^2\times3.

Full working

23×3=242^3\times3=24, so the LCM is 24.

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