4024/12 Oct/Nov 2023, Question 9: Prime Factorization
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Write 180 as a product of primes, then use the given prime factor forms of 36 and N with their LCM to determine the value of k.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Express 180 as a product of its prime factors.
- 1180 = 2 × 90 = 2 × 2 × 45 = 2 × 2 × 3 × 15 = 2 × 2 × 3 × 3 × 5
- 2180 = 2² × 3² × 5
Answer2² × 3² × 5 or 2 × 2 × 3 × 3 × 5
Part (b) · 1 mark
Given 36 = 2² × 3² and N = 2² × 3 × k with k > 3, and 180 as the LCM of 36 and N, find k.
- 1LCM = 2² × 3² × k = 180 = 2² × 3² × 5
- 2k = 5
Answer5
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 LemmaraMore past-paper questions on prime factorization
Also searched as: 4024/12/O/N/23 · 4024_w23_qp_12 · 4024 w23 12 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.