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4MA1/1FR Jun 2019, Question 18: Prime Factorization

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

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The question, in short

Work with the numbers 21, 35 and 720: find their shared factor, break 720 into primes, and find a multiplier making a square.

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

Part (a) · 1 mark

Determine the largest integer that divides both 21 and 35 exactly.

  1. 121 = 3 × 7
  2. 235 = 5 × 7
  3. 3HCF = 7

Answer7

Part (b) · 3 marks

Express 720 as a multiplication of prime numbers, showing each step of the method.

  1. 1720 = 2 × 360
  2. 2360 = 2 × 180
  3. 3180 = 2 × 90
  4. 490 = 2 × 45
  5. 545 = 3 × 15
  6. 615 = 3 × 5
  7. 7So 720 = 2 × 2 × 2 × 2 × 3 × 3 × 5

Answer2 × 2 × 2 × 2 × 3 × 3 × 5

Part (c) · 1 mark

Identify the least whole number which, times 720, yields a perfect square.

  1. 1720 = 2⁴ × 3² × 5
  2. 2For a square number, all prime exponents must be even
  3. 3The exponent of 5 is 1, so multiply by 5 to make it 2
  4. 4Smallest whole number is 5

Answer5

Stuck on a step? Read the free lesson: Prime Factorization

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