[discia] GCSE Maths › Number › Prime Factors, HCF and LCM

Prime Factors, HCF and LCM

discia.org 10 questions · 30 marks
Name Date
  1. Either paper 2 marks

    Write \(1404\) as a product of its prime factors.

    Give your answer in index form.

    Show answer
    \(2^{ 2 } \times 3^{ 3 } \times 13\)
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  2. Either paper 3 marks

    Express \(224\) as a product of its prime factors, giving your answer in index form.

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    \(2^{5} \times 7\)
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  3. Either paper 1 mark

    Calculate the lowest common multiple (LCM) of \(9\), \(12\) and \(39\).

    Show answer
    \(468\)
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  4. Either paper 2 marks

    Show that \(1625\) can be written as a cube number multiplied by a prime number between \(10\) and \(15\).

    Show answer
    \(1625 = 5^3 \times 13\), where \(5^3 = 125\) is a cube number and \(13\) is prime with \(10 < 13 < 15\)
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  5. Either paper 2 marks

    Two numbers \(m\) and \(n\) are such that

    \(m\) is an even number

    \(n\) is a multiple of 5

    the highest common factor (HCF) of \(m\) and \(n\) is \(9\)

    Write down a possible value for \(m\) and a possible value for \(n\).

    Show answer
    Any pair that meets all three conditions, for example \(m = 18\) and \(n = 45\)
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  6. Either paper 2 marks

    Written as the product of prime factors, \(4312 = 2^3 \times 7^2 \times 11\) and \(6468 = 2^2 \times 3 \times 7^2 \times 11\).

    Find the highest common factor (HCF) of \(4312\) and \(6468\).

    Give your answer as an integer.

    Show answer
    \(2156\)
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  7. Either paper 6 marks

    \(A = 216\) and \(B = 144\)

    (a)

    Express \(A\) as a product of its prime factors. Give your answer in index form.

    (b)

    Work out the highest common factor (HCF) of \(A\) and \(B\).

    (c)

    Work out the lowest common multiple (LCM) of \(A\) and \(B\).

    Show answer
    (a) \(2^{ 3 } \times 3^{ 3 }\)
    (b) \(72\)
    (c) \(432\)
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  8. Either paper 5 marks

    Cupcakes are sold in packs of \(16\).

    Paper cases are sold in packs of \(28\).

    Omar wants to buy exactly the same number of each, with none left over.

    (a)

    Find the smallest number of cupcakes he can buy.

    (b)

    How many packs of each does he buy?

    Show answer
    (a) \(112\)
    (b) 7 packs of cupcakes and 4 packs of paper cases
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  9. Either paper 5 marks

    A rectangular wall is \(24\) cm wide and \(108\) cm high.

    It is to be covered completely with identical square tiles. No gaps are allowed and no tile may be cut.

    (a)

    Work out the largest possible side length of a tile.

    (b)

    How many of these tiles are needed?

    Show answer
    (a) \(12\ \text{cm}\)
    (b) \(18\)
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  10. Either paper 2 marks

    \(x\) is a whole number greater than \(14\).

    \(x\) leaves a remainder of \(2\) when it is divided by \(3\), by \(4\) and by \(14\).

    Work out the smallest possible value of \(x\), and the next smallest.

    Show answer
    \(86\) and \(170\)
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discia.org Prime Factors, HCF and LCM · sheet 1
Answers Prime Factors, HCF and LCM · sheet 1
  1. \(2^{ 2 } \times 3^{ 3 } \times 13\)
  2. \(2^{5} \times 7\)
  3. \(468\)
  4. \(1625 = 5^3 \times 13\), where \(5^3 = 125\) is a cube number and \(13\) is prime with \(10 < 13 < 15\)
  5. Any pair that meets all three conditions, for example \(m = 18\) and \(n = 45\)
  6. \(2156\)
  7. (a) \(2^{ 3 } \times 3^{ 3 }\)
    (b) \(72\)
    (c) \(432\)
  8. (a) \(112\)
    (b) 7 packs of cupcakes and 4 packs of paper cases
  9. (a) \(12\ \text{cm}\)
    (b) \(18\)
  10. \(86\) and \(170\)
discia.org Prime Factors, HCF and LCM · sheet 1