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4MA1/1FR Jan 2019, Question 24: Prime Factorization

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

Using N = 480 × 10⁹, express it in standard form, give its prime factorisation in index form with working, and identify the greatest odd divisor.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Rewrite 480 × 10⁹ in standard form.

  1. 1480 = 4.8 × 10², so N = 4.8 × 10² × 10⁹
  2. 2N = 4.8 × 10¹¹

Answer4.8 × 10¹¹

Part (b) · 3 marks

Express 480 × 10⁹ as a product of prime powers, showing each step of the working.

  1. 1480 = 2⁵ × 3 × 5, so N = 2⁵ × 3 × 5 × 10⁹
  2. 210⁹ = (2 × 5)⁹ = 2⁹ × 5⁹
  3. 3N = 2⁵⁺⁹ × 3 × 5¹⁺⁹
  4. 4N = 2¹⁴ × 3 × 5¹⁰

Answer2¹⁴ × 3 × 5¹⁰

Part (c) · 1 mark

Determine the greatest odd number that divides 480 × 10⁹ exactly.

  1. 1N = 2¹⁴ × 3 × 5¹⁰; an odd factor has no factor of 2
  2. 2Largest odd factor = 3 × 5¹⁰
  3. 35¹⁰ = 9 765 625
  4. 43 × 9 765 625 = 29296875

Answer29296875

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