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4MA1/1F Jun 2019, Question 14: HCF and LCM

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 4 marks

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The question, in short

Work with the numbers 40 and 64 and the expression A = 2ⁿ × 3 × 5ᵐ, finding a shared factor and rewriting 8A in prime-power form.

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Part (a) · 2 marks

Determine the largest integer that divides both 40 and 64 exactly.

  1. 140 = 2 × 2 × 2 × 5
  2. 264 = 2 × 2 × 2 × 2 × 2 × 2
  3. 3Common prime factors: 2 × 2 × 2 = 8

Answer8

Part (b) · 2 marks

Express 8A using only prime bases raised to powers, in terms of n and m.

  1. 18 = 2³
  2. 28A = 2³ × 2ⁿ × 3 × 5ᵐ
  3. 3Add the powers of 2: 2³⁺ⁿ × 3 × 5ᵐ

Answer2ⁿ⁺³ × 3 × 5ᵐ

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