Chapter Summary

Classifying and factorising

• Prime: exactly two factors. Composite: more than two. $1$ is neither.
• Test a number by dividing by the primes up to $\sqrt{n}$.
• Every composite has ONE prime factorisation, by factor tree or repeated division.

Reading the indices

• HCF: common primes only, at the smallest index.
• LCM: every prime, at the largest index.
• Perfect square: all indices even; halve them for the root.
• Perfect cube: all indices multiples of $3$; divide by $3$ for the root.

Later: LCM comes back as the common denominator (Sec 2, Algebraic Fractions)