Factors, multiples, and primes (age 11+) · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Prime factorisation, HCF, and LCM

Mathematics · Multiplication & Division · ages 11-12
Name ______________________   Date ____________

  1. Use prime factorization to find the LCM (lowest common multiple) of 8 and 12.

    Answer: ______________

  2. Which is the correct prime factorisation of 20 written in index notation?

    • 2² × 5
    • 2 × 5²
    • 2³ × 5

  3. Two students break 90 into primes in a different order. If both work correctly, they end up with the same set of prime factors.

    Circle one:   True   False

  4. What number does 3² × 5 represent?

    • 15
    • 45
    • 30

  5. Use prime factorization to find the HCF (highest common factor) of 24 and 36.

    Answer: ______________

  6. What is the prime factorization of 72, written in index notation?

    • 2³ × 3²
    • 2² × 3³
    • 2³ × 3
    • 2 × 3⁴

  7. What is the prime factorization of 60, written in index notation?

    • 2 × 3 × 5
    • 2² × 3 × 5
    • 2² × 3²
    • 2 × 3² × 5

  8. Use prime factorization to find the GCF of 32 and 80.

    Answer: ______________

  9. Priya finds the HCF of 18 = 2 × 3² and 45 = 3² × 5, but multiplies 3² × 5 by mistake. What should she multiply instead to get the correct HCF?

    • 2 × 5
    • 3² alone
    • 2 × 3² × 5

  10. What is the greatest common factor of 54 and 81?

    • 27
    • 9
    • 18
    • 3
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Prime factorisation, HCF, and LCM W1-mt_xhoOWnhtHq-s1

  1. 24 · The LCM is built from the highest power of every prime that shows up in either number.
  2. 2² × 5 · 20 = 2 × 2 × 5, and two 2s multiplied together is written 2² in index notation.
  3. True · Unique factorisation means every number has exactly one set of prime factors, no matter the order you divide in.
  4. 45 · 3² means 3 × 3 = 9, and 9 × 5 = 45.
  5. 12 · The HCF is built from the lowest matching power of every prime the two numbers share.
  6. 2³ × 3² · 72 splits into 2 × 2 × 2 × 3 × 3. Three 2s become 2³ and two 3s become 3².
  7. 2² × 3 × 5 · 60 breaks down into 2 × 2 × 3 × 5. Since the 2 repeats twice, you write it as 2².
  8. 16 · 32 and 80 only share the prime 2, so the GCF comes from the lowest matching power of 2.
  9. 3² alone · Only 3 is common to both 18 and 45. Multiplying 3² alone gives the HCF, 9. The primes 2 and 5 aren't shared, so they don't belong.
  10. 27 · 54 and 81 only share the prime 3, so the GCF comes from the lowest matching power of 3.
Worksheet · LightMySky