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4MA1/1F Jun 2020, Question 23: Prime Factorization

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 3 marks

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The question, in short

Given A = 2 × 3⁴³ and B = 16 × 3³⁷, work with these two numbers in prime factor form to find their HCF and to write A × B using prime powers.

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Part (a) · 1 mark

Using the prime factor forms of A and B, determine the largest number dividing both.

  1. 1B = 16 × 3³⁷ = 2⁴ × 3³⁷
  2. 2Lowest power of 2 in both: 2¹
  3. 3Lowest power of 3 in both: 3³⁷
  4. 4HCF = 2 × 3³⁷

Answer2 × 3³⁷

Part (b) · 2 marks

Multiply A by B and give the result as prime powers in simplest form.

  1. 1A = 2 × 3⁴³ and B = 16 × 3³⁷ = 2⁴ × 3³⁷
  2. 2A × B = 2¹ × 2⁴ × 3⁴³ × 3³⁷
  3. 3Add the powers: 2⁵ × 3⁸⁰

Answer2⁵ × 3⁸⁰

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