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Year 9 · Key Stage 3 · free KS3 maths worksheet

Primes, HCF and LCM

12 original questions, 38 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 all the factors of 36.
  2. Write down the first five multiples of 7.
  3. Here is a list of numbers.
    15   23   27   31   39   49
    Write down the prime numbers in the list.
3 marks
Show answer
a) 1, 2, 3, 4, 6, 9, 12, 18, 36 b) 7, 14, 21, 28, 35 c) 23, 31
2

Meera says

"Every multiple of 5 ends in the digit 5."

Give an example to show that Meera is wrong.

2 marks
Show answer
Any multiple of 5 ending in 0, e.g. 10
3
  1. Write down all the common factors of 24 and 40.
  2. Write down the first three common multiples of 6 and 8.
3 marks
Show answer
a) 1, 2, 4, 8 b) 24, 48, 72
4
  1. By listing factors, find the highest common factor (HCF) of 18 and 30.
  2. By listing multiples, find the lowest common multiple (LCM) of 18 and 30.
3 marks
Show answer
a) 6 b) 90
5

Work out how many positive whole numbers less than 100 are multiples of both 4 and 6.

3 marks
Show answer
8
6
  1. Write 180 as a product of its prime factors. Give your answer in index form.
  2. Write 350 as a product of its prime factors. Give your answer in index form.
3 marks
Show answer
a) 22 × 32 × 5 b) 2 × 52 × 7
7

Write down two numbers, both greater than 20, whose highest common factor (HCF) is 7

2 marks
Show answer
Any valid pair, e.g. 21 and 28 (21 = 3 × 7 and 28 = 4 × 7, and 3 and 4 share no common factor greater than 1, so HCF = 7).
8

60 = 2 × 2 × 3 × 5
84 = 2 × 2 × 3 × 7

  1. Complete the Venn diagram to show the prime factors of 60 and 84.
  2. Use your Venn diagram to find the highest common factor (HCF) of 60 and 84.
  3. Use your Venn diagram to find the lowest common multiple (LCM) of 60 and 84.
6084
4 marks
Show answer
a) 5 | 2, 2, 3 | 7 b) 12 c) 420
9

A = 23 × 3 × 52

B = 22 × 32 × 5

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

    Give your answers as products of powers of primes.

3 marks
Show answer
a) 22 × 3 × 5 = 60 b) 23 × 32 × 52 = 1800
10
  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 × 32 × 7 b) 1260
11
  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 × 7 b) 56
12
  1. Miss Khan has 48 pencils and 72 rulers. She puts all of them into packs so that every pack is the same. She makes as many packs as possible. How many packs does she make, and what is in each pack?
  2. A number 12 bus leaves the school every 12 minutes. A number 20 bus leaves the school every 20 minutes. Both buses leave the school at 08:00. When is the next time they both leave the school together?
4 marks
Show answer
a) 24 packs of 2 pencils and 3 rulers b) 09:00

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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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