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0580/32 May/Jun 2024, Question 1: HCF and LCM

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 10 marks

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The question, in short

From a given list of numbers, identify a factor of 21, a square number and a prime number; then evaluate several numerical expressions, insert brackets to make an equation true, and find the LCM of 30 and 68.

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

Part (ai) · 1 mark

Pick from the list a number that divides 21 exactly.

  1. 121 = 3 × 7, so 7 is a factor of 21

Answer7

Part (aii) · 1 mark

Pick from the list a number that is a square number.

  1. 149 = 7²

Answer49

Part (aiii) · 1 mark

Pick from the list a number that is prime.

  1. 17 has only factors 1 and 7, so it is prime

Answer7

Part (bi) · 1 mark

Work out the cube root of 1728.

  1. 112 × 12 × 12 = 1728, so ∛1728 = 12

Answer12

Part (bii) · 1 mark

Work out the value of 2 to the power 5.

  1. 12⁵ = 2 × 2 × 2 × 2 × 2 = 32

Answer32

Part (biii) · 1 mark

Work out the value of 5 to the power 0.

  1. 1Any non-zero number to the power 0 is 1: 5⁰ = 1

Answer1

Part (biv) · 1 mark

Work out the value of 36 to the power one half.

  1. 136^(1/2) = √36 = 6

Answer6

Part (c) · 1 mark

Insert one pair of brackets into 3 × 2 − 6 − 2 ÷ 2 so the result equals 4.

  1. 13 × 2 − (6 − 2) ÷ 2 = 6 − 4 ÷ 2 = 6 − 2 = 4

Answer3 × 2 − (6 − 2) ÷ 2 = 4

Part (d) · 2 marks

Find the lowest common multiple of 30 and 68.

  1. 130 = 2 × 3 × 5 and 68 = 2² × 17
  2. 2LCM = 2² × 3 × 5 × 17 = 1020

Answer1020

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Also searched as: 0580/32/M/J/24 · 0580_s24_qp_32 · 0580 s24 32 · question 1.
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