GCSE · Integers, powers & roots

Factors, multiples and prime numbersExam-style questions

What a factor and a multiple are and how to keep them the right way round, how to list every factor of a number in pairs, why 1 is not prime and 2 is the only even prime, the primes up to 50, square and cube numbers on sight, and how one counter-example settles an "Is she correct?" question.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4
  1. 1
    Rhys says,

    "All prime numbers are odd."

    Mai says,

    "If you add 11 to a square number, the answer is always a prime number."
    (a) Explain why Rhys is wrong.

    (1 mark)
    (b) Show that Mai is wrong.

    (1 mark)
    Level 3 · 2 marksTry it
  2. 2
    Leah is asked to write down all the factors of a number.

    Here is her list.

    12481020401 \qquad 2 \qquad 4 \qquad 8 \qquad 10 \qquad 20 \qquad 40

    Leah has missed out one factor.
    (a) What is the number?

    (1 mark)
    (b) Which factor has Leah missed out?

    (1 mark)
    Level 3 · 2 marksTry it
  3. 3
    Owen is thinking of a number.
    • It is a factor of 3636
    • It is a multiple of 44
    • It is not a square number.
    Work out Owen's number.

    (2 marks)
    Level 3 · 2 marksTry it
  4. 4
    A teacher has 6060 chairs.

    She puts all the chairs in equal rows, with no chairs left over.

    Each row has at least 77 chairs and at most 1515 chairs.

    Work out all the possible numbers of chairs in each row.

    (3 marks)
    Level 3 · 3 marksTry it
  5. 5
    Hana says,

    "There are four prime numbers between 8080 and 100100."

    Is Hana correct?

    Show how you decide.

    (3 marks)
    Level 3 · 3 marksTry it