Knowledge Organiser: Factors, Multiples and Primes
Key Terms
- Factor: A number that divides exactly into another with no remainder
- Multiple: A number in the times table of another number
- Prime number: A number greater than 1 with exactly two factors: 1 and itself
- HCF: Highest Common Factor: largest factor shared by two numbers
- LCM: Lowest Common Multiple: smallest positive multiple shared by two numbers
- Prime factorisation: Writing a number as a product of its prime factors
Must-Know Facts
- 1 is NOT a prime number (has only one factor)
- 2 is the only even prime number
- Primes up to 20: 2, 3, 5, 7, 11, 13, 17, 19
- HCF cannot be larger than the smaller of the two numbers
- LCM cannot be smaller than the larger of the two numbers
- HCF × LCM = product of the two original numbers
- To check if n is prime: test divisibility by primes up to √n
Key Methods
- Finding factors: use factor pairs (1×n, 2×?, 3×?…) until pairs repeat
- Prime factorisation: factor tree (split until all branches are prime)
- HCF: take common prime factors with LOWEST powers
- LCM: take ALL prime factors with HIGHEST powers
Key Formulas
- HCF × LCM = product of the two original numbers
- Prime factorisation: write n = 2ᵃ × 3ᵇ × 5ᶜ × …
- Test for prime: check divisibility by primes up to √n
Common Mistakes
- Listing factors in wrong order: Always list factors in pairs from smallest to largest: 1 × 12, 2 × 6, 3 × 4
- Confusing HCF and LCM: HCF is the biggest number that divides into both; LCM is the smallest number both divide into: draw a Venn diagram of prime factors to keep them separate
- Forgetting 1 is not prime: 1 has only one factor (itself), so it is not prime: primes have exactly two factors
- Incomplete prime factorisation: Always circle each prime and keep dividing until you cannot divide further: missing a factor gives a wrong HCF/LCM