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Year 7 · Key Stage 3 · free KS3 maths worksheet

Factors, multiples, primes, HCF and LCM

12 original questions, 31 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

List all the factors of 28.

2 marks
Show answer
1, 2, 4, 7, 14, 28
2

Find all the factor pairs of 60

2 marks
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1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10
3

List all the prime numbers between 20 and 35.

2 marks
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23, 29, 31
4
  1. Write down all the common factors of 24 and 36
  2. Write down the first three common multiples of 6 and 8
3 marks
Show answer
a) 1, 2, 3, 4, 6, 12 b) 24, 48, 72
5

Find the highest common factor (HCF) of 48 and 84

2 marks
Show answer
12
6

Find the lowest common multiple (LCM) of 15 and 18

3 marks
Show answer
90
7

For each problem, write down whether you would use the highest common factor (HCF) or the lowest common multiple (LCM). You do not need to solve them.

  1. Two buses leave the school at 8 am. One returns every 12 minutes and the other every 18 minutes. When are they next back at the school together?
  2. Two ribbons, 45 cm and 60 cm long, are cut into pieces that are all the same length, with nothing left over. What is the longest each piece can be?
2 marks
Show answer
a) LCM b) HCF
8

Write 84 as a product of its prime factors.

2 marks
Show answer
22 × 3 × 7
9

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

3 marks
Show answer
23 × 32 × 5
10

Mr Hussain has 42 pencils and 56 rubbers.

He puts them all into identical packs, with nothing left over.

  1. What is the greatest number of packs he can make?
  2. How many pencils and how many rubbers are in each pack?
3 marks
Show answer
a) 14 b) 3 pencils and 4 rubbers
11

Two warning buoys are anchored in a harbour.

One buoy flashes every 24 seconds.

The other buoy flashes every 40 seconds.

At 8 pm the two buoys flash at the same time.

Work out how many seconds later the two buoys next flash at the same time.

3 marks
Show answer
120 seconds
12

180 = 22 × 32 × 5

84 = 22 × 3 × 7

  1. Complete the Venn diagram to show the prime factors of 180 and 84
  2. Find the highest common factor (HCF) of 180 and 84
  3. Find the lowest common multiple (LCM) of 180 and 84
18084
4 marks
Show answer
a) 180 only: 3, 5; both: 2, 2, 3; 84 only: 7 b) 12 c) 1260

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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