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
$2520 = 2^3 \times 3^2 \times 5 \times 7$

(a) Write 5040 as a product of prime factors in index form.

(b) Write 252 as a product of prime factors in index form.
Level 4 · 2 marksTry it
2
$k = 2^3 \times 3 \times 5^2$

(a) Explain why $k$ is not a square number.

(b) Find the smallest whole number $n$ such that $kn$ is a square number.
Level 4 · 3 marksTry it
3
$p = 2^4 \times 3 \times 5^3$

(a) Explain how you can tell that 12 is a factor of $p$ .

(b) Find the largest square number that is a factor of $p$ .
Level 4 · 3 marksTry it
4
$780 = 2^2 \times 3 \times 5 \times 13$

Use this fact to write each of the following as a product of prime factors in index form.

(a) $1560$

(b) $390$
Level 4 · 2 marksTry it
5
$n = 2^3 \times 3^5 \times 5^2$

Find the smallest whole number that $n$ must be multiplied by to give a square number.
Level 4 · 3 marksTry it

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