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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 PrimesDownload 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 1212 and 1818.

Working

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

Prime factors.

Worked example 2 — Prime test

Is 9191 prime?

Working

91=7×13⇒not prime91=7\times13\Rightarrow\text{not prime}

Test primes up to 91\sqrt{91}.

Worked example 3 — Product of primes

Express 8484 as a product of primes.

Working

22×3×72^2\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 SheetAnswers PDF
WorksheetsTopic summariesTopic videos