Key Tips:
- Factor pairs: Always work systematically to avoid missing factors
- Prime factors: 1 is NOT a prime number (has only 1 factor, not 2)
- HCF: Cannot be larger than the smaller number
- LCM: Cannot be smaller than the larger number
- Check: HCF × LCM = product of the two numbers
Common Mistakes:
- ❌ Forgetting that 1 and the number itself are always factors
- ❌ Thinking 1 is prime (it's neither prime nor composite)
- ❌ Confusing HCF and LCM (HCF divides both, LCM is divisible by both)
- ❌ Not using systematic methods for large numbers
- ❌ Making arithmetic errors in factor trees
Memory Aids:
- FACTORS: "Divide IN" - factors divide into the number
- MULTIPLES: "Times table" - multiply the number
- HCF: "Highest that goes into both"
- LCM: "Lowest that both go into"
This exam tips covers Exam Tips & Common Mistakes 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 8 of 9 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
Practice questions for Factors, Multiples & Primes
Which of these numbers is prime?
Explain why 51 is not a prime number.
Quick recall flashcards
Multiple
A number in the times table of another number.
Example: Multiples of 5 are 5, 10, 15, 20, 25, 30...
Factor
A number that divides exactly into another number with no remainder.
Example: Factors of 12 are 1, 2, 3, 4, 6, 12