Types of number: past paper questions

Where the questions come from

• Question 11May/June 2026, paper 12Structured4 marks

  Write 400 as a product of its prime factors.

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• Question 14Oct/Nov 2024, paper 11Structured3 marks

  Write 360 as a product of its prime factors.

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• Question 14Oct/Nov 2023, paper 11Structured5 marks

  Write 36 as a product of its prime factors.

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• Question 4Oct/Nov 2025, paper 12Structured2 marks

  Petra thinks of a number. The number is a multiple of 7. Petra says: When I write my number correct to the nearest ten it is 30.

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• Question 12Oct/Nov 2024, paper 12Structured1 mark

  Here is a list of numbers. $$\frac{1}{3}\sqrt{4}{2}^0\sqrt{5}\frac{10}{8}{2}^{-1}$$ Write down the number in the list that is irrational.

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• Question 9Oct/Nov 2023, paper 12Structured3 marks

  Write 180 as the product of its prime factors.

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• Question 14May/June 2023, paper 12Structured4 marks

  Write 325 as a product of its prime factors.

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• Question 15Oct/Nov 2025, paper 21Structured2 marks

  x = 2² × 3ⁿ⁺¹ × 7 y = 2ⁿ × 3ⁿ × 7⁴ n is a positive integer greater than 2. Find the highest common factor (HCF) of x and y. Write your answer as the product of prime factors in terms of n. x = 2² × 3ⁿ⁺¹ × 7 y = 2ⁿ × 3ⁿ × 7⁴ n is a positive integer greater than 2.

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• Question 6May/June 2024, paper 12Structured2 marksHas a diagram

  Jack uses number cards to make a 2-digit number. Complete the missing card to give a 2-digit number that is not a prime number.

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• Question 14Oct/Nov 2025, paper 22Structured4 marks

  $N=2\times 3^x\times 5^y$ The lowest common multiple (LCM) of $N$ and 360 is 16200. Find the value of $x$ and the value of $y$.

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• Question 4May/June 2024, paper 21Structured5 marks

  Two of the factors of 50 are square numbers. One of these square numbers is 1. Find the other square number that is a factor of 50.

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• Question 10May/June 2025, paper 12Structured3 marks

  Write 228 as a product of its prime factors.

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• Question 2May/June 2025, paper 22Structured3 marks

  Write eighteen thousand and twelve in figures.

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