Printable · GCSE Foundation · ages 14-16

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

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 Foundation

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

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1.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
2.Which of these numbers is a common factor of 18 and 24?
(a)6
(b)8
(c)12
(d)9
3.Write 200 as a product of its prime factors, using index notation.
(a)2 × 5³
(b)2³ × 5
(c)2² × 5³
(d)2³ × 5²
4.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
5.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.
(a)6
(b)72
(c)60
(d)12
6.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
7.Work out the highest common factor of 12 and 18.
(a)2
(b)6
(c)36
(d)3
8.Is 120 divisible by 5? Give a reason for your answer.
(a)Yes, because 120 ends in 0
(b)No, because 1 + 2 + 0 = 3 is not a multiple of 5
(c)Yes, because 120 is even
(d)No, because 5 does not divide into 12
9.Work out the lowest common multiple of 4 and 6.
(a)12
(b)2
(c)6
(d)24
10.Work out how many factors 36 has.
(a)5
(b)10
(c)8
(d)9
11.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
12.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
13.Work out the highest common factor of 20 and 32.
(a)8
(b)4
(c)2
(d)160
14.Work out the highest common factor of 15 and 25.
(a)75
(b)5
(c)15
(d)3
15.Write 12 as a product of its prime factors.
(a)2² × 3
(b)2 × 3²
(c)2 × 3
(d)2 × 6

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