Lemmara logoLemmaraWorked solution

4024/12 May/Jun 2025, Question 10: Prime Factorization

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Express 228 in prime factor form, then use the given fact that 228 squared equals 51984 to express 51984 in prime factor form.

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

Part (a) · 2 marks

Give the prime factorisation of 228.

  1. 1228 = 2 × 114 = 2 × 2 × 57 = 2 × 2 × 3 × 19
  2. 2228 = 2² × 3 × 19

Answer2² × 3 × 19 or 2 × 2 × 3 × 19

Part (b) · 1 mark

Using 228² = 51984, give the prime factorisation of 51984.

  1. 151 984 = 228² = (2² × 3 × 19)²
  2. 2= 2⁴ × 3² × 19²

Answer2⁴ × 3² × 19² or 2 × 2 × 2 × 2 × 3 × 3 × 19 × 19

Stuck on a step? Read the free lesson: Prime Factorization

Practise more prime factorization questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on prime factorization

Also searched as: 4024/12/M/J/25 · 4024_s25_qp_12 · 4024 s25 12 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.