Topic summary · IGCSE handout

Factors and Primes summary

Prime factorisation, HCF and LCM unlock fraction work, surds and index laws later.

Open Learning Sheet — Factors and Primes Download Factors and Primes answers PDF

Files: 21_factors_and_primes_handout.pdf · 21_factors_and_primes_handout_answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

Prime numbers have exactly two distinct factors: 1 and themselves.
HCF: take lowest powers of shared primes; LCM: highest powers of all primes appearing.
Divisibility tests speed up factor trees.

Worked example 1 — HCF and LCM

HCF and LCM of $12$ and $18$ .

Working

\mathrm{HCF}=6,\ \mathrm{LCM}=36

Prime factors.

Worked example 2 — Prime test

Is $91$ prime?

Working

91=7\times13\Rightarrow\text{not prime}

Test primes up to $\sqrt{91}$ .

Worked example 3 — Product of primes

Express $84$ as a product of primes.

Working

2^2\times3\times7

Factor tree.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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