Day 2 · Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic: every composite number can be expressed as a product of primes, and this factorisation is unique (apart from the order of the factors).

140 factorised into primes is 2² × 5 × 7 (since 4×5×7 = 140).

We can use prime factorisation to find the HCF (take the smallest power of common factors) and LCM (take the largest power of all factors present).

12 = 2²×3 and 18 = 2×3² — HCF = 2×3 = 6 and LCM = 2²×3² = 36.

Activity: Try prime-factorising 60, then check that HCF×LCM of 12 and 18 equals 12×18.