Prime Factors, HCF and LCM worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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2 marks
Write \(1404\) as a product of its prime factors.
Give your answer in index form.
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6 marks
\(A = 800\) and \(B = 1000\)
(a)Express \(A\) as a product of its prime factors. Give your answer in index form.
(b)Find the highest common factor (HCF) of \(A\) and \(B\).
(c)Find the lowest common multiple (LCM) of \(A\) and \(B\).
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5 marks
Cupcakes are sold in packs of \(10\).
Paper cases are sold in packs of \(15\).
Yusuf wants to buy exactly the same number of each, with none left over.
(a)Calculate the smallest number of cupcakes he can buy.
(b)How many packs of each does he buy?
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5 marks
A rectangular wall is \(25\) cm wide and \(45\) cm high.
It is to be covered completely with identical square tiles. No gaps are allowed and no tile may be cut.
(a)Find the largest possible side length of a tile.
(b)How many of these tiles are needed?
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3 marks
\(N = 2^{ 3 } \times 3^{ 3 }\)
Work out the smallest whole number \(k\) so that \(N \times k\) is a square number.
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2 marks
Express \(1008\) as a product of its prime factors.
Give your answer in index form.
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6 marks
\(A = 400\) and \(B = 500\)
(a)Express \(A\) as a product of its prime factors. Give your answer in index form.
(b)Find the highest common factor (HCF) of \(A\) and \(B\).
(c)Find the lowest common multiple (LCM) of \(A\) and \(B\).
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5 marks
Cupcakes are sold in packs of \(12\).
Paper cases are sold in packs of \(28\).
Zainab wants to buy exactly the same number of each, with none left over.
(a)Calculate the smallest number of cupcakes she can buy.
(b)How many packs of each does she buy?
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5 marks
A rectangular wall is \(30\) cm wide and \(54\) cm high.
It is to be covered completely with identical square tiles. No gaps are allowed and no tile may be cut.
(a)Calculate the largest possible side length of a tile.
(b)How many of these tiles are needed?
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3 marks
\(N = 2^{ 2 } \times 3^{ 3 }\)
Find the smallest whole number \(k\) so that \(N \times k\) is a square number.
Answers
- \(2^{ 2 } \times 3^{ 3 } \times 13\)
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(a) \(2^{ 5 } \times 5^{ 2 }\)
(b) \(200\)
(c) \(4000\) -
(a) \(30\)
(b) 3 packs of cupcakes and 2 packs of paper cases -
(a) \(5\ \text{cm}\)
(b) \(45\) - \(6\)
- \(2^{ 4 } \times 3^{ 2 } \times 7\)
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(a) \(2^{ 4 } \times 5^{ 2 }\)
(b) \(100\)
(c) \(2000\) -
(a) \(84\)
(b) 7 packs of cupcakes and 3 packs of paper cases -
(a) \(6\ \text{cm}\)
(b) \(45\) - \(3\)