Printable · GCSE Higher · ages 14-16

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.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
2.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
3.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
4.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
5.Write 90 as a product of its prime factors.
(a)2 × 3² × 5
(b)2 × 45
(c)2 × 3 × 15
(d)3 × 3 × 10
6.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.
(a)12
(b)7
(c)20
(d)5
7.Work out how many factors 100 has.
(a)8
(b)4
(c)9
(d)10
8.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.
(a)7
(b)14
(c)2
(d)168
9.Write 12 as a product of its prime factors.
(a)2² × 3
(b)2 × 3²
(c)2 × 3
(d)2 × 6
10.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
11.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.
12.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
13.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.
(a)36
(b)6
(c)108
(d)216
14.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.
(a)120
(b)12
(c)1440
(d)60
15.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

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