4024/11 Oct/Nov 2024, Question 14: Prime Factorization
Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Express 360 using only prime factors, then determine the least positive integer n for which 360n becomes a perfect cube.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Break 360 down into a multiplication of primes.
- 1360 = 2 × 180 = 2 × 2 × 90 = 2 × 2 × 2 × 45 = 2 × 2 × 2 × 3 × 3 × 5
- 2360 = 2³ × 3² × 5
Answer2³ × 3² × 5 or 2 × 2 × 2 × 3 × 3 × 5
Part (b) · 1 mark
Give the least positive n making 360n a cube.
- 1For a cube every power must be a multiple of 3: need one more 3 and two more 5s
- 2n = 3 × 5² = 75
Answer75
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Also searched as: 4024/11/O/N/24 · 4024_w24_qp_11 · 4024 w24 11 · question 14.
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