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 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 8
Practice
14 questions
Recall
22 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