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0580/21 May/Jun 2026, Question 10: Prime Factorization

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 3 marks

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The question, in short

Use given prime factorisations of 24 192 and 245 000 to find their HCF, then express 20k² in prime factor form in terms of prime c.

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Part (a) · 1 mark

Find the highest common factor of 24 192 and 245 000 using their prime factor decompositions.

  1. 1Common primes with lowest powers: 2³ and 7
  2. 2HCF = 2³ × 7 = 56

Answer56

Part (b) · 2 marks

Given k = 2³ × 3⁴ × 5 × c², write 20k² as a product of prime factors, simplified, in terms of c.

  1. 1k² = 2⁶ × 3⁸ × 5² × c⁴
  2. 220 = 2² × 5
  3. 320k² = 2⁸ × 3⁸ × 5³ × c⁴

Answer2⁸ × 3⁸ × 5³ × c⁴

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Also searched as: 0580/21/M/J/26 · 0580_s26_qp_21 · 0580 s26 21 · question 10.
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