Year 10 factors, multiples, primes and HCF/LCM test to download as PDF

This Year 10 factors, multiples, primes and HCF/LCM test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 14-15, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Factors and primes
Non-calculator.
1. Write down all the factors of 30. (2 marks)
2. Write down all the prime numbers between 10 and 30. (2 marks)
Question 2 – Prime factors, HCF and LCM
Non-calculator.
1. Write 420 as a product of its prime factors. (2 marks)
2. Find the HCF and the LCM of 420 and 504. (2 marks)
Question 3 – Problem: the bus timetable
Bus 11 leaves the depot every 20 minutes. Bus 12 leaves every 30 minutes. They both leave at 07:00.
1. At what time do they next leave together? (2 marks)
2. How many times between 07:00 and 10:00 (including 07:00) do the two buses leave at the same time? (2 marks)
Question 4 – Problem: the tiled wall
A rectangular wall measures 270 cm by 180 cm. It is covered with identical square tiles with no gaps and no cutting.
1. Find the side of the largest square tile that can be used. (2 marks)
2. How many of these tiles are needed? (2 marks)
Question 5 – Higher: counting and proof
Higher tier.
1. A PIN has 4 digits chosen from 0 to 9. Digits can be repeated. How many PINs are possible? (1 mark)
2. How many PINs have 4 different digits? (1 mark)
3. Prove that the sum of any three consecutive whole numbers is a multiple of 3. (2 marks)

How to use this Year 10 factors, multiples, primes and HCF/LCM test

First, revise with the factors, multiples, primes and HCF/LCM lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the factors, multiples, primes and HCF/LCM test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 10 factors, multiples, primes and HCF/LCM test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.

Factors, multiples, primes and HCF/LCM – Year 10 GCSE maths test to download as PDF

Question 1 – Factors and primes

Question 2 – Prime factors, HCF and LCM

Question 3 – Problem: the bus timetable

Question 4 – Problem: the tiled wall

Question 5 – Higher: counting and proof

How to use this Year 10 factors, multiples, primes and HCF/LCM test

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