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4024/12 May/Jun 2023, Question 14: Prime Factorization

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Express 325 as a product of primes, then for P = xⁿy² and Q = xⁿ⁻¹y⁴ with prime x and y, determine the HCF in terms of x, y and n.

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Part (a) · 2 marks

Break down 325 into its prime factors.

  1. 1325 = 5 × 65
  2. 265 = 5 × 13
  3. 3325 = 5 × 5 × 13 = 5² × 13

Answer5² × 13 or 5 × 5 × 13

Part (b) · 2 marks

Given P = xⁿy² and Q = xⁿ⁻¹y⁴ with prime x and y, find the HCF expressed using x, y and n.

  1. 1Lower power of x: xⁿ and xⁿ⁻¹ give xⁿ⁻¹
  2. 2Lower power of y: y² and y⁴ give y²
  3. 3HCF = xⁿ⁻¹y²

Answerxⁿ⁻¹y²

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