Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Prime factorisation

Writing a number as a product of primes.

16 original questions, 46 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Is 51 a prime number? Give a reason for your answer.

2 marks
Show answer
No, 51 = 3 x 17
2

Write 84 as a product of its prime factors.

2 marks
Show answer
22 x 3 x 7
3

Here is part of a factor tree for 90.

90 splits into 9 and 10. 9 splits into 3 and A. 10 splits into B and 5. All the numbers at the ends of the branches are prime.

  1. Work out the values of A and B.
  2. Write 90 as a product of its prime factors.
3 marks
Show answer
a) A = 3, B = 2 b) 2 x 32 x 5
4

Write 264 as a product of its prime factors.

2 marks
Show answer
23 x 3 x 11
5

Here is a list of numbers.

8   14   19   27   35

Write down the number from the list that is a prime number.

1 mark
Show answer
19
6

Is 97 a prime number? Show how you know.

2 marks
Show answer
Yes, 97 is not divisible by 2, 3, 5 or 7
7
  1. Write 168 as a product of its prime factors.
  2. Write 252 as a product of its prime factors.
  3. Work out the highest common factor (HCF) of 168 and 252.
3 marks
Show answer
a) 23 x 3 x 7 b) 22 x 32 x 7 c) 84
8

A = 23 × 3 × 5    and    B = 22 × 32 × 7

  1. Find the lowest common multiple (LCM) of A and B.
  2. Find the highest common factor (HCF) of A and B.

Give each answer as an ordinary number.

4 marks
Show answer
a) 2520 b) 12
9

Use prime factors to show that 1764 is a square number.

3 marks
Show answer
1764 = 22 x 32 x 72 = (2 x 3 x 7)2 = 422
10
  1. Write 90 and 150 as products of prime factors, in index form.
  2. Find the highest common factor (HCF) of 90 and 150.
  3. Find the lowest common multiple (LCM) of 90 and 150.
5 marks
Show answer
a) 90 = 2 x 32 x 5 and 150 = 2 x 3 x 52 b) 30 c) 450
11

72 is multiplied by a whole number n to give a square number.

Find the smallest possible value of n, and the square number.

3 marks
Show answer
n = 2, square number 144
12

120 = 23 × 3 × 5

Write 1200 as a product of its prime factors.

3 marks
Show answer
24 x 3 x 52
13

Write 360 as a product of powers of its prime factors.

3 marks
Show answer
23 x 32 x 5
14

List all the prime numbers between 20 and 35.

2 marks
Show answer
23, 29, 31
15
  1. Write 126 as a product of its prime factors.
  2. Find the lowest common multiple (LCM) of 126 and 60
4 marks
Show answer
a) 2 x 32 x 7 b) 1260
16
  1. Write 448 as a product of powers of its prime factors.
  2. Find the highest common factor (HCF) of 448 and 168
4 marks
Show answer
a) 26 x 7 b) 56

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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