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Year 8 · Key Stage 3 · free KS3 maths worksheet

Primes, HCF and LCM

12 original questions, 36 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
  1. Write down the first ten prime numbers.
  2. Explain why 2 is the only even prime number.
  3. Here is a list of numbers.
    21   31   39   41   51
    Write down the numbers from the list that are prime.
3 marks
Show answer
a) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 b) Every even number bigger than 2 can be divided by 2, so it has more than two factors c) 31 and 41
2

Find two prime numbers that add together to make 32.

2 marks
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3 and 29 (or 13 and 19)
3
  1. Write down all the factor pairs of 60.
  2. Write down all the common factors of 60 and 42.
3 marks
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a) 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 × 10 b) 1, 2, 3, 6
4

Find the highest common factor (HCF) of 54 and 90

2 marks
Show answer
18
5
  1. Find the two common multiples of 6 and 8 that are between 50 and 100.
  2. Find the lowest common multiple (LCM) of 4, 6 and 10.
3 marks
Show answer
a) 72 and 96 b) 60
6

Write 264 as a product of its prime factors.

2 marks
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23 × 3 × 11
7
  1. Write 600 as a product of its prime factors. Give your answer in index form.
  2. Hence write 1200 as a product of its prime factors in index form.
3 marks
Show answer
a) 23 × 3 × 52 b) 24 × 3 × 52
8

Priya has two ribbons. One is 84 cm long and the other is 126 cm long.

She cuts both ribbons into pieces that are all the same length, with no ribbon left over. She wants the pieces to be as long as possible.

  1. Work out the length of each piece.
  2. How many pieces does she get altogether?
3 marks
Show answer
a) 42 cm b) 5
9

Nadia is making table decorations.

Each decoration needs one candle and one holder.

Candles are sold in packs of 9

Holders are sold in packs of 12

Nadia buys exactly the same number of candles as holders, with none left over.

Work out the smallest number of packs of candles and the smallest number of packs of holders she can buy.

3 marks
Show answer
candles) 4 packs holders) 3 packs
10
  1. Find the highest common factor (HCF) of 72 and 120
  2. Find the lowest common multiple (LCM) of 72 and 120
4 marks
Show answer
a) 24 b) 360
11

180 = 2 × 2 × 3 × 3 × 5 and 84 = 2 × 2 × 3 × 7

  1. Complete the Venn diagram to show the prime factors of 180 and 84.
  2. Use your Venn diagram to find the highest common factor (HCF) of 180 and 84.
  3. Use your Venn diagram to find the lowest common multiple (LCM) of 180 and 84.
ξ18084
4 marks
Show answer
a) 180 only: 3, 5; both: 2, 2, 3; 84 only: 7 b) 12 c) 1260
12

20 = 2 × 2 × 5    30 = 2 × 3 × 5    42 = 2 × 3 × 7

  1. Complete the Venn diagram to show the prime factors of 20, 30 and 42.
  2. Write down the highest common factor of 20, 30 and 42.
  3. Three lights on a stage flash every 20 seconds, every 30 seconds and every 42 seconds. They all flash together at the start of a show. How many minutes later do all three next flash together?
ξ203042
4 marks
Show answer
a) all three: 2; 20 and 30 only: 5; 30 and 42 only: 3; 20 only: 2; 42 only: 7; 30 only: empty b) 2 c) 7 minutes

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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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