Key Stage 3 (KS3) · Mathematics

Factors, Multiples and Primes: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Factors, Multiples and Primes.

10 questions24 marksFree, no account

Question 1

1 mark

Find the highest common factor (HCF) of 18, 42 and 72.

Question 2

1 mark

Find the highest common factor (HCF) of 24 and 60.

Question 3

1 mark

Which of the following numbers is a prime number?

Question 4

1 mark

Which of the following is the lowest common multiple (LCM) of 12, 18, and 30?

Question 5

1 mark

Find the least common multiple (LCM) of 15, 20 and 30.

Question 6

2 marks

What is the smallest prime number greater than 20?

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

Determine if 157 is a prime number.

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Question 8

6 marks

The prime factorization of a number is \( 2^x \cdot 3^2 \cdot 5 \). If the number is 360, find the value of \( x \) and then determine the total number of factors this number has.

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Question 9

4 marks

Consider the integers 84 and 126.
(a) Express each number as a product of its prime factors in index form.
(b) Find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of 84 and 126.

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

Consider the numbers 42 and 70.
(a) Express both numbers as products of their prime factors.
(b) Find the Highest Common Factor (HCF) of 42 and 70.

Write your answer out first, then check it against the worked solution.

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