GCSE · Integers, powers & roots

Prime factorisationExam-style questions

Why every whole number breaks into a unique product of primes, how to find it with a factor tree, and how the prime form answers divisibility and square-number questions instantly.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
$360 = 2^3 \times 3^2 \times 5$

Find the smallest whole number that 360 must be multiplied by to give a cube number.
Level 5 · 3 marksTry it
2
$N = 2^3 \times 5^2$

(a) Write down the value of $N$ .

(b) Work out how many factors $N$ has in total.

Hint: every factor of $N$ has the form $2^a \times 5^b$ .
Level 5 · 3 marksTry it