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0580/32 Oct/Nov 2024, Question 2: HCF and LCM

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 17 marks

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The question, in short

From a list of numbers, identify odd, factor of 28, square, prime, and multiple of 9; then evaluate powers, prime factorisation, cube root, estimation, standard form, and a lap timing problem.

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

Part (ai) · 1 mark

Pick an odd number from the list.

  1. 141 is a whole number not divisible by 2
  2. 241 (or 117 or 121)

Answer41 or 117 or 121

Part (aii) · 1 mark

Pick a number from the list that divides 28.

  1. 128 ÷ 14 = 2
  2. 214

Answer14

Part (aiii) · 1 mark

Pick a square number from the list.

  1. 111² = 121
  2. 2121

Answer121

Part (aiv) · 1 mark

Pick a prime number from the list.

  1. 141 has no factors other than 1 and 41
  2. 241

Answer41

Part (av) · 1 mark

Pick a multiple of 9 from the list.

  1. 19 × 13 = 117
  2. 2117

Answer117

Part (b) · 1 mark

State the value of 5⁰.

  1. 1Any non-zero number to the power 0 is 1
  2. 25⁰ = 1

Answer1

Part (c) · 2 marks

Express 60 as a product of prime factors.

  1. 160 = 2 × 30
  2. 230 = 2 × 15
  3. 315 = 3 × 5
  4. 460 = 2² × 3 × 5

Answer2 × 2 × 3 × 5 or 2² × 3 × 5

Part (d) · 1 mark

Work out the cube root of 157464.

  1. 1∛157 464 on the calculator
  2. 2= 54

Answer54

Part (e) · 2 marks

Round each value to 1 significant figure and estimate (67.8 × 2.38) ÷ (4.803 + 29.87), showing working.

  1. 167.8 ≈ 70, 2.38 ≈ 2, 4.803 ≈ 5, 29.87 ≈ 30
  2. 2(70 × 2)/(5 + 30) = 140/35
  3. 3= 4

Answer4

Part (fi) · 1 mark

Compare 9.78 × 10⁸ and 2.04 × 10⁹, stating which is larger and why.

  1. 19.78 × 10⁸ = 978 000 000
  2. 22.04 × 10⁹ = 2 040 000 000
  3. 32.04 × 10⁹ is larger because it has the larger power of 10

Answer2.04 × 10⁹ and it has the larger power of 10

Part (fii) · 2 marks

Calculate (1.732 × 10³) ÷ (5.73 × 10⁻¹) and give the answer in standard form.

  1. 11.732 × 10³ = 1732, 5.73 × 10⁻¹ = 0.573
  2. 21732 ÷ 0.573 = 3022.6…
  3. 3= 3.02 × 10³

Answer3.02 × 10³ or 3.023 × 10³

Part (g) · 3 marks

Two cars lap in 96 s and 120 s, starting together at 08 37; find the next time they start a lap together.

  1. 196 = 2⁵ × 3, 120 = 2³ × 3 × 5
  2. 2LCM = 2⁵ × 3 × 5 = 480 seconds
  3. 3480 s = 8 minutes
  4. 408 37 + 8 min = 08 45

Answer08 45

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Also searched as: 0580/32/O/N/24 · 0580_w24_qp_32 · 0580 w24 32 · question 2.
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