This deep dive covers Advanced Techniques within Factors, Multiples & Primes for GCSE Mathematics. Revise Factors, Multiples & Primes in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 9 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Advanced Techniques
Venn Diagram Method for HCF and LCM
For numbers like 12 and 18:
- 12 = 2² × 3
- 18 = 2 × 3²
HCF: Take the intersection (common factors with lowest powers)
HCF = 2¹ × 3¹ = 6
LCM: Take the union (all factors with highest powers)
LCM = 2² × 3² = 4 × 9 = 36
Quick Prime Check
To check if n is prime, test divisibility by primes up to √n:
- For n = 97: √97 ≈ 9.8, so test 2, 3, 5, 7
- 97 ÷ 2 = 48.5 (not divisible)
- 97 ÷ 3 = 32.33... (not divisible)
- 97 ÷ 5 = 19.4 (not divisible)
- 97 ÷ 7 = 13.86... (not divisible)
- Therefore 97 is prime
Practice questions for Factors, Multiples & Primes
Which of these numbers is prime?
Explain why 51 is not a prime number.