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.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.
2.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
3.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
4.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
5.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
6.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
7.Write 200 as a product of its prime factors, using index notation.
(a)2 × 5³
(b)2³ × 5
(c)2² × 5³
(d)2³ × 5²
8.Work out how many factors 36 has.
(a)5
(b)10
(c)8
(d)9
9.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
10.Write down a prime number between 30 and 40.
(a)33
(b)31
(c)36
(d)34
11.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
12.Which statement about the number 51 is correct?
(a)51 is prime, because it is not divisible by 2, 3 or 5.
(b)51 is not prime, because it is divisible by 2.
(c)51 is prime, because it is an odd number.
(d)51 is not prime, because 51 = 3 × 17.
13.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
14.Work out the highest common factor of 20 and 32.
(a)8
(b)4
(c)2
(d)160
15.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

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