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Year 8 Mathematics · Prime factors and index notation

Name: ______________________

Date: ____________

  1. 1. Which of these numbers is prime?

    • ☐ (a) 21
    • ☐ (b) 27
    • ☐ (c) 29
    • ☐ (d) 33

  2. 2. How is 3 × 3 × 3 × 3 written in index notation?

    • ☐ (a) 3⁴
    • ☐ (b) 4³
    • ☐ (c) 12
    • ☐ (d) 3 × 4

  3. 3. Which is the prime factorisation of 36?

    • ☐ (a) 2² × 3²
    • ☐ (b) 4 × 9
    • ☐ (c) 2 × 3 × 6
    • ☐ (d) 2³ × 3

  4. 4. What is the value of 2⁵?

    • ☐ (a) 10
    • ☐ (b) 25
    • ☐ (c) 32
    • ☐ (d) 7

  5. 5. Write 60 as a product of prime factors using index notation.

  6. 6. Is 51 a prime number or a composite number?

  7. 7. Which number has the prime factorisation 2³ × 5?

  8. 8. Write 72 as a product of prime factors using index notation.

Answer sheet

  1. 1. 29 — 29 has only the factors 1 and 29. The others are composite: 21 = 3 × 7, 27 = 3 × 9 and 33 = 3 × 11.
  2. 2. 3⁴ — The base 3 is multiplied by itself 4 times, so it is 3⁴.
  3. 3. 2² × 3² — 36 = 2 × 2 × 3 × 3 = 2² × 3². The options 4 × 9 and 2 × 3 × 6 contain composite numbers, and 2³ × 3 = 24.
  4. 4. 32 — 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. It is not 2 × 5 = 10.
  5. 5. 2² × 3 × 5 — 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5, which is 2² × 3 × 5.
  6. 6. Composite — The digits add to 5 + 1 = 6, a multiple of 3, so 51 = 3 × 17. It has more than two factors, so it is composite.
  7. 7. 40 — 2³ = 2 × 2 × 2 = 8, and 8 × 5 = 40.
  8. 8. 2³ × 3² — 72 = 2 × 36 = 2 × 2 × 18 = 2 × 2 × 2 × 9 = 2 × 2 × 2 × 3 × 3, which is 2³ × 3².

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