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0580/41 May/Jun 2025, Question 10: Factors and Multiples

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 6 marks

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The question, in short

List the factors of 18, factorise 3y − xy + 15 − 5x, then use both results to find positive integers x and y satisfying 3y − xy + 15 − 5x = 18.

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

Part (a) · 2 marks

Write down every factor of 18.

  1. 118 = 1 × 18 = 2 × 9 = 3 × 6
  2. 2Factors: 1, 2, 3, 6, 9, 18

Answer1, 2, 3, 6, 9, 18

Part (b) · 2 marks

Factorise the expression 3y − xy + 15 − 5x.

  1. 13y − xy + 15 − 5x = y(3 − x) + 5(3 − x)
  2. 2= (y + 5)(3 − x)

Answer(y + 5)(3 − x)

Part (c) · 2 marks

Using parts (a) and (b), find one positive integer x and its matching y making the expression equal 18.

  1. 1(y + 5)(3 − x) = 18 with x, y positive integers, so 3 − x is 1 or 2
  2. 23 − x = 1: x = 2, y + 5 = 18, y = 13
  3. 33 − x = 2: x = 1, y + 5 = 9, y = 4
  4. 4x = 2, y = 13 or x = 1, y = 4

Answerx = 2, y = 13 or x = 1, y = 4

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Also searched as: 0580/41/M/J/25 · 0580_s25_qp_41 · 0580 s25 41 · question 10.
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