DIV016 · Factors, multiples & divisibility · Classes 6–9
Factor trees
A factor tree splits a number into two factors, then splits those again, until every branch ends in a prime. The primes at the ends multiply to give the number.
84 → 2·2·3·7Factor trees
📐 Formula
n = product of the primes at the ends of the branches
✏️ Worked example
84 → 2 × 42 → 2 × 2 × 21 → 2 × 2 × 3 × 7 = 2² × 3 × 7.
🌍 Where it is used
Finding HCF and LCM, simplifying fractions and roots.
❓ Quick check
Which are the leaves of a factor tree for 30?
🏋️ Practice
EasyPrime factors of 18?
Answer: 2 × 3²
MediumPrime factors of 100?
Answer: 2² × 5²
ChallengePrime factors of 196?
Answer: 2² × 7²