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Factors, multiples, primes, HCF and LCM worksheet — GCSE Higher

Fifteen questions on "factors, multiples, primes, hcf and lcm" — DfE statement N4. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Factors, multiples, primes, HCF and LCM worksheet — GCSE Higher

Maths · GCSE Higher · N4 · Factors, multiples, primes, HCF and LCM · Non-calculator · 15 questions

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1.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.
(a)24
(b)12
(c)48
(d)96
2.Which statement about the number 91 is correct?
(a)91 is not prime, because 91 = 7 × 13.
(b)91 is prime, because it is not divisible by 2, 3 or 5.
(c)91 is not prime, because it is divisible by 3.
(d)91 is prime, because it is an odd number ending in 1.
3.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.
(a)30, which is not prime
(b)31, which is not prime because 31 = 1 × 31
(c)31, which is not prime because it is a multiple of 3
(d)31, which is prime
4.Write 90 as a product of its prime factors.
(a)2 × 3² × 5
(b)2 × 45
(c)2 × 3 × 15
(d)3 × 3 × 10
5.Write 12 as a product of its prime factors.
(a)2² × 3
(b)2 × 3²
(c)2 × 3
(d)2 × 6
6.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.
(a)36
(b)18
(c)54
(d)27
7.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.
(a)12
(b)240
(c)16
(d)15
8.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.
(a)12
(b)3
(c)6
(d)252
9.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.
(a)4
(b)24
(c)96
(d)20
10.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.
(a)16
(b)30
(c)60
(d)2
11.Write 60 as a product of its prime factors, using index notation.
(a)2 × 3 × 5
(b)2² × 3 × 5
(c)2 × 3 × 5²
(d)2² × 3² × 5
12.Work out how many factors 36 has.
(a)5
(b)10
(c)8
(d)9
13.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.
(a)30 cm
(b)360 cm
(c)15 cm
(d)10 cm
14.Work out how many factors 100 has.
(a)8
(b)4
(c)9
(d)10
15.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.
(a)18 minutes
(b)54 minutes
(c)3 minutes
(d)15 minutes

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