Factors and Multiples 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.

10 questions 33 marks Sheet 1

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3 marks
(a)
Write down the first five multiples of \(4\).

(b)
Work out the lowest common multiple (LCM) of \(4\) and \(14\).
4 marks
(a)
Work out the highest common factor (HCF) of \(40\) and \(50\).

(b)
Work out the lowest common multiple (LCM) of \(40\) and \(50\).
3 marks
In a light display the amber light flashes every \(16\) seconds and the green light flashes every \(36\) seconds.

The two lights flash together at the start of the display.

Work out how long it is until they next flash together.
3 marks
Devan has \(50\) marbles and \(60\) counters.

He makes identical bags, using all of the marbles and all of the counters.

Calculate the largest number of bags he can make.
4 marks
(a)
Express \(45\) as a product of its prime factors. Give your answer in index form.

(b)
Find the highest common factor (HCF) of \(45\) and \(165\).
3 marks
Two numbers are written as products of prime factors.

(a)
\(P = 2^{ 5 } \times 3^{ 2 } \times 5^{ 3 }\) and \(Q = 2^{ 3 } \times 3^{ 4 } \times 5^{ 2 }\)

State the highest common factor (HCF) of \(P\) and \(Q\) as a product of prime factors.

(b)
Write down the lowest common multiple (LCM) of \(P\) and \(Q\) as a product of prime factors.
3 marks
(a)
Write down the first five multiples of \(4\).

(b)
Find the lowest common multiple (LCM) of \(4\) and \(14\).
4 marks
(a)
Work out the highest common factor (HCF) of \(35\) and \(40\).

(b)
Work out the lowest common multiple (LCM) of \(35\) and \(40\).
3 marks
In a light display the red light flashes every \(25\) seconds and the green light flashes every \(35\) seconds.

The two lights flash together at the start of the display.

Calculate how long it is until they next flash together.
3 marks
Isla has \(55\) crayons and \(77\) pens.

She makes identical bags, using all of the crayons and all of the pens.

Find the largest number of bags she can make.

Answers

(a) 4, 8, 12, 16, 20
(b) \(28\)
(a) \(10\)
(b) \(200\)
\(144\ \text{seconds}\)
\(10\)
(a) \(3^{ 2 } \times 5\)
(b) \(15\)
(a) \(2^{ 3 } \times 3^{ 2 } \times 5^{ 2 }\)
(b) \(2^{ 5 } \times 3^{ 4 } \times 5^{ 3 }\)
(a) 4, 8, 12, 16, 20
(b) \(28\)
(a) \(5\)
(b) \(280\)
\(175\ \text{seconds}\)
\(11\)

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