Factors, Primes, Powers and Roots summary

Key learning points

• Square numbers and cube numbers — recognise them quickly.
• Between which integers does $\sqrt{50}$ lie?
• Prime factorisation helps rewrite powers cleanly.

Worked example 1 — Prime factorisation

Write $60$ as a product of primes.

Working

Factor tree.

Worked example 2 — HCF and LCM

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

Working

From prime factors.

Worked example 3 — Estimate a root

Between which integers is $\sqrt{50}$?

Working

$7^2=49$, $8^2=64$.

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.