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0580/33 May/Jun 2024, Question 4: Factors and Multiples

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 11 marks

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The question, in short

Answer nine short number questions covering place value, factors, primes, roots, multiples, reciprocals, fractions, irrational numbers and HCF.

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

Part (a) · 1 mark

State the value of the digit 8 in the number 39 829.

  1. 1The 8 is in the hundreds column: 800

Answer800

Part (b) · 2 marks

List every factor of 18.

  1. 1Factor pairs: 1 × 18, 2 × 9, 3 × 6
  2. 2Factors: 1, 2, 3, 6, 9, 18

Answer1 2 3 6 9 18

Part (c) · 1 mark

Demonstrate that 57 is not a prime number.

  1. 157 = 3 × 19, so 57 has factors other than 1 and 57: not prime

Answer57 = 3 × 19

Part (d) · 1 mark

Given √x = 64, find the value of x.

  1. 1x = 64² = 4096

Answer4096

Part (e) · 1 mark

Identify the smallest multiple of 40 that exceeds 620.

  1. 140 × 15 = 600, 40 × 16 = 640
  2. 2First multiple above 620 is 640

Answer640

Part (f) · 1 mark

Find the reciprocal of the fraction 2/3.

  1. 1Reciprocal of 2/3 = 3/2 = 1 1/2

Answer1 1/2 or 1.5

Part (g) · 1 mark

Give a fraction whose value lies between 1/5 and 1/4.

  1. 11/5 = 8/40 and 1/4 = 10/40
  2. 29/40 lies between them

AnswerAny correct fraction

Part (h) · 1 mark

Write an irrational number between 9 and 10.

  1. 19² = 81 and 10² = 100, so √90 lies between 9 and 10
  2. 2√90 is irrational

AnswerAny correct irrational number

Part (i) · 2 marks

Calculate the highest common factor of 72 and 180.

  1. 172 = 2³ × 3² and 180 = 2² × 3² × 5
  2. 2HCF = 2² × 3² = 36

Answer36

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Also searched as: 0580/33/M/J/24 · 0580_s24_qp_33 · 0580 s24 33 · question 4.
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