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4024/11 Oct/Nov 2022, Question 11: Prime Factorization

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Express 120 in prime factor form, then use the given factorisation of 315 to find the least n making 315n a perfect square.

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

Part (a) · 2 marks

Give 120 broken down into a multiplication of primes.

  1. 1120 = 2 × 60 = 2 × 2 × 30 = 2 × 2 × 2 × 15 = 2 × 2 × 2 × 3 × 5
  2. 2= 2³ × 3 × 5

Answer2 × 2 × 2 × 3 × 5 or 2³ × 3 × 5

Part (b) · 1 mark

Given 315 = 3² × 5 × 7, determine the smallest whole number n for which 315n is a square.

  1. 1For a square every prime power must be even: 5 and 7 need another factor each
  2. 2n = 5 × 7 = 35

Answer35

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Also searched as: 4024/11/O/N/22 · 4024_w22_qp_11 · 4024 w22 11 · question 11.
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