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4MA1/1HR Jun 2024, Question 11: HCF and LCM

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

Given A = 2⁵ × 5 × 7² and B = 2³ × 5³ × 7⁴, find the HCF of 5A and 2B, and the value of (AB)², both as products of prime factors.

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Part (a) · 2 marks

Find the highest common factor of 5A and 2B, giving the result as a product of prime factors.

  1. 1A = 2⁵ × 5 × 7², so 5A = 2⁵ × 5² × 7²
  2. 2B = 2³ × 5³ × 7⁴, so 2B = 2⁴ × 5³ × 7⁴
  3. 3For the HCF take the lower power of each prime.
  4. 4For 2: the lower of 2⁵ and 2⁴ is 2⁴
  5. 5For 5: the lower of 5² and 5³ is 5²
  6. 6For 7: the lower of 7² and 7⁴ is 7²
  7. 7The HCF of 5A and 2B is 2⁴ × 5² × 7²

Answer2⁴ × 5² × 7²

Part (b) · 2 marks

Calculate (AB)² and express the answer as a product of prime factors.

  1. 1AB = (2⁵ × 5 × 7²) × (2³ × 5³ × 7⁴)
  2. 2Add the powers of each prime: AB = 2^(5+3) × 5^(1+3) × 7^(2+4) = 2⁸ × 5⁴ × 7⁶
  3. 3Squaring doubles each power: (AB)² = 2^(8×2) × 5^(4×2) × 7^(6×2)
  4. 4(AB)² = 2¹⁶ × 5⁸ × 7¹²

Answer2¹⁶ × 5⁸ × 7¹²

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