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4024/12 Oct/Nov 2022, Question 10: Prime Factorization

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Express 420 as a product of primes, then use the given prime factorisation of 1512 to find the HCF of 420 and 1512.

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Part (a) · 2 marks

Write 420 as a product of its prime factors.

  1. 1420 = 2 × 210 = 2 × 2 × 105
  2. 2105 = 3 × 35 = 3 × 5 × 7
  3. 3420 = 2² × 3 × 5 × 7

Answer2² × 3 × 5 × 7 or 2 × 2 × 3 × 5 × 7

Part (b) · 1 mark

Using 1512 = 2³ × 3³ × 7, find the highest common factor of 420 and 1512.

  1. 1420 = 2² × 3 × 5 × 7 and 1512 = 2³ × 3³ × 7
  2. 2Common prime factors: 2² × 3 × 7
  3. 3HCF = 4 × 3 × 7 = 84

Answer84

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Also searched as: 4024/12/O/N/22 · 4024_w22_qp_12 · 4024 w22 12 · question 10.
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