Maths Library

Prime Numbers and Prime Factorisation: Year 8 maths

Identify prime and composite numbers and decompose integers into their prime factorisations. Pupils construct factor trees and write prime factor expressions using index notation.

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What this covers

Prime Numbers and Prime Factorisation is taught in Year 8 (age 12 to 13, KS3) as a main teaching focus. It sits in the Number strand.

Worked example

Write 60 as a product of its prime factors using index notation.

  1. Divide 60 by lowest prime 2: 60 = 2 × 30
  2. Divide 30 by 2: 30 = 2 × 15
  3. Divide 15 by 3: 15 = 3 × 5 (both are prime)
  4. Write in index form: 2^2 × 3 × 5

Answer: 2^2 × 3 × 5

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Identify prime and composite numbers up to 30
  2. Identify prime numbers up to 100
  3. Find prime factors of 2-digit numbers using factor trees
  4. Write prime factorisation of numbers up to 150 in index form
  5. Find prime factorisations of numbers up to 500 and solve prime-based puzzles

Common mistakes

  • Thinking 1 is a prime number or that all odd numbers are prime
  • Leaving composite factors in a prime factor tree (e.g. writing 60 as 4 * 15)

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Find highest common factors, lowest common multiples, and prime factorisations of integers.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Prime Numbers and Prime Factorisation

Year 8 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Is 55 a prime number? Write yes or no.
[3]
2.
Is 128 a prime number? Write yes or no.
[3]
3.
Is 53 a prime number? Write yes or no.
[3]
4.
Is 91 a prime number? Write yes or no.
[3]
5.
Is 47 a prime number? Write yes or no.
[3]
6.
Is 146 a prime number? Write yes or no.
[3]

Answer key

  1. no55 is divisible by 5, so it has another factor
  2. no128 is divisible by 2, so it has another factor
  3. yes53 has only two factors, 1 and 53
  4. no91 is divisible by 7, so it has another factor
  5. yes47 has only two factors, 1 and 47
  6. no146 is divisible by 2, so it has another factor