[discia] GCSE Maths › Number › Factors and Multiples

Factors and Multiples

discia.org 10 questions · 20 marks
Name Date
  1. Either paper 1 mark

    Circle the factor of \(48\).

    \(5\)   \(144\)   \(18\)   \(13\)   \(8\)

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    \(8\)
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  2. Either paper 3 marks
    (a)

    Write down the first five multiples of \(15\).

    (b)

    Work out the lowest common multiple (LCM) of \(15\) and \(25\).

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    (a) 15, 30, 45, 60, 75
    (b) \(75\)
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  3. Either paper 1 mark

    Here is a list of numbers.

    57, 77, 105, 112, 162

    One of these numbers is a multiple of \(21\).

    Which number?

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    \(105\)
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  4. Either paper 3 marks

    Answer both parts.

    (a)

    Write down all the factors of \(55\).

    (b)

    Amara says, “When two multiples of 7 are added, the answer is always a multiple of 14.”

    Give one example to show that she is wrong.

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    (a) \(1,\ 5,\ 11,\ 55\)
    (b) \(14 + 35 = 49\), which is not a multiple of \(14\) (any two multiples of 7 with one odd and one even multiplier will do)
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  5. Either paper 3 marks

    Here are three statements about whole numbers.

    (a)

    A prime number can be a multiple of 3.

    Give one example to show that this is correct.

    (b)

    The product of two even numbers is always a multiple of 8.

    Give one example to show that this is not correct.

    (c)

    A square number can be a multiple of 8.

    Give one example to show that this is correct.

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    (a) Any valid example, for instance: \(3\) is a prime number and \(3 = 3 \times 1\), so it is a multiple of \(3\).
    (b) Any valid example, for instance: \(2 \times 6 = 12\) and \(12 \div 8 = 1.5\), so \(12\) is not a multiple of \(8\); \(2\) and \(6\) are both even.
    (c) Any valid example, for instance: \(16 = 4^2\) and \(16 = 8 \times 2\), so \(16\) is a square number and a multiple of \(8\).
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  6. Either paper 1 mark

    Here are four numbers.

    \(8 \qquad 9 \qquad 19 \qquad 36\)

    Which of these numbers has exactly two factors?

    Circle your answer.

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    \(19\)
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  7. Either paper 1 mark
    Here are four numbers.
    3273648
    Circle the number that is a multiple of both \(12\) and \(9\).
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    \(36\)
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  8. Either paper 2 marks
    Here are five circles arranged in a cross. The vertical line and the horizontal line each have three circles and share the middle one.
    ◯
    ◯ ◯ ◯
    ◯
    Put the numbers \(2,\ 3,\ 4,\ 6,\ 12\) into the circles so that * each line of three numbers multiplies to \(144\) * the total of the horizontal line is one more than the total of the vertical line. Use each number once.
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    middle circle \(12\); vertical line \(3\), \(12\), \(4\) (top and bottom in either order); horizontal line \(2\), \(12\), \(6\) (left and right in either order)
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  9. Either paper 3 marks

    \(c\) and \(d\) are positive whole numbers.

    \(c\) is even.

    \(d\) is odd.

    Tick a box for each expression to show whether it is even, odd or if you cannot tell.

    (a)

    Is \(\frac{ 2c + 2 }{2}\) even, odd or can you not tell?

    (b)

    Is \(d^2 + 1\) even, odd or can you not tell?

    (c)

    Is \(\frac{ 10d }{2}\) even, odd or can you not tell?

    Show answer
    (a) odd
    (b) even
    (c) odd
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  10. Either paper 2 marks

    Find the multiple of \(62\) that is nearest to \(524\).

    Show answer
    \(496\)
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discia.org Factors and Multiples · sheet 1
Answers Factors and Multiples · sheet 1
  1. \(8\)
  2. (a) 15, 30, 45, 60, 75
    (b) \(75\)
  3. \(105\)
  4. (a) \(1,\ 5,\ 11,\ 55\)
    (b) \(14 + 35 = 49\), which is not a multiple of \(14\) (any two multiples of 7 with one odd and one even multiplier will do)
  5. (a) Any valid example, for instance: \(3\) is a prime number and \(3 = 3 \times 1\), so it is a multiple of \(3\).
    (b) Any valid example, for instance: \(2 \times 6 = 12\) and \(12 \div 8 = 1.5\), so \(12\) is not a multiple of \(8\); \(2\) and \(6\) are both even.
    (c) Any valid example, for instance: \(16 = 4^2\) and \(16 = 8 \times 2\), so \(16\) is a square number and a multiple of \(8\).
  6. \(19\)
  7. \(36\)
  8. middle circle \(12\); vertical line \(3\), \(12\), \(4\) (top and bottom in either order); horizontal line \(2\), \(12\), \(6\) (left and right in either order)
  9. (a) odd
    (b) even
    (c) odd
  10. \(496\)
discia.org Factors and Multiples · sheet 1