Factors, Multiples & Primes

MathematicsAQAEdexcelGCSEUnit: Number
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The basics

Building Blocks of Numbers

Building Blocks of Numbers

Every whole number can be built from prime numbers - they're like the atoms of maths! Understanding factors (what divides into a number) and multiples (the times tables) helps with everything from simplifying fractions to solving real-world problems like tiling floors and scheduling events.
Factor: A number that divides exactly into another number with no remainder. Example: Factors of 12 are 1, 2, 3, 4, 6, 12
Key terms

Mathematics glossary

Factor
A number that divides exactly into another number with no remainder. Example: Factors of 12 are 1, 2, 3, 4, 6, 12
Multiple
A number in the times table of another number. Example: Multiples of 5 are 5, 10, 15, 20, 25, 30...
Exam tip

Earn the mark scheme marks

Exam Tips & Common Mistakes

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"

Now try it yourself

Quiz · Question 1 of 14

Which of these numbers is prime?

Tap an answer to check it

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