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4024/12 Oct/Nov 2021, Question 9: Prime Factorization

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Express 216 as a product of primes, then use LCM 216 and HCF 18 to find two integers above 25.

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Part (a) · 2 marks

Break down 216 into its prime factors.

  1. 1216 = 2 × 108 = 2 × 2 × 54 = 2 × 2 × 2 × 27
  2. 2= 2 × 2 × 2 × 3 × 3 × 3 = 2³ × 3³

Answer2³ × 3³ or 2 × 2 × 2 × 3 × 3 × 3

Part (b) · 2 marks

Given LCM 216 and HCF 18, determine the two integers, each larger than 25.

  1. 1HCF 18 = 2 × 3², so the numbers are 18a and 18b with a, b sharing no factor
  2. 2LCM = 18ab = 216 → ab = 12, so a = 3, b = 4 (1 and 12 gives 18, not > 25)
  3. 318 × 3 = 54 and 18 × 4 = 72

Answer54 and 72

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Also searched as: 4024/12/O/N/21 · 4024_w21_qp_12 · 4024 w21 12 · question 9.
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