Lemmara logoLemmaraWorked solution

0580/32 Feb/Mar 2025, Question 19: Prime Factorization

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 3 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Express the number 2025 in two different ways: first by breaking it into prime factors, then by splitting it into a pair of square numbers each above 1.

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

Part (a) · 2 marks

Give 2025 broken down into its prime factors, multiplied together.

  1. 12025 = 5 × 405 = 5 × 5 × 81
  2. 281 = 3 × 3 × 3 × 3
  3. 32025 = 3⁴ × 5²

Answer3⁴ × 5²

Part (b) · 1 mark

Find two square numbers, each larger than 1, whose product equals 2025.

  1. 13⁴ = 81 = 9² and 5² = 25
  2. 22025 = 25 × 81

Answer25 × 81 or 225 × 9

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

Practise more prime factorization questions

Real 0580 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: 0580/32/F/M/25 · 0580_m25_qp_32 · 0580 m25 32 · question 19.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.