Learning pack · Foundation · CIE Core

Factors, Primes, Powers and Roots

What's in this pack: printable worksheet PDF, matching answers PDF (Foundation · CIE Core depth). Powers and roots sit alongside primes and factors: square numbers, cubes, and estimating roots without a calculator.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

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Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 📖 Full summary

Files: foundation-17 Factors, Primes, Powers and Roots.pdf · foundation-17 Factors, Primes, Powers and Roots answers.pdf

Full topic summary

Powers and roots sit alongside primes and factors: square numbers, cubes, and estimating roots without a calculator.

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

60=2^2\times3\times5

Factor tree.

Worked example 2 — HCF and LCM

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

Working

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

From prime factors.

Worked example 3 — Estimate a root

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

Working

7\text{ and }8

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

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