Prime Factors, HCF & LCMCambridge IGCSE Maths: Subtopic test

1. 1
   $60 = 2^2 \times 3 \times 5$ and $84 = 2^2 \times 3 \times 7$.

   (a)

   Find the HCF of 60 and 84.

   [1 mark]

   • A6
   • B12
   • C24
   • D420

   (b)

   Find the LCM of 60 and 84.

   [1 mark]

   • A140
   • B210
   • C420
   • D5040

   (c)

   How many prime factors does 60 have in total, counting repeats (e.g. $2^2$ counts as two)?

   [1 mark]

   • A3
   • B4
   • C5
   • D6

   Total for question 1: 3 marks

2. 2
   Two bus routes leave a station together at 8:00 am. Route A departs every 18 minutes and Route B departs every 24 minutes.

   (a)

   Find the LCM of 18 and 24 using prime factors, and hence state the next time after 8:00 am that both routes will depart together.

   [2 marks]

   (b)

   Find the HCF of 18 and 24 using prime factors.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A gardener has 90 tulip bulbs and 126 daffodil bulbs. She wants to plant them in identical rows containing only one type of bulb per row, with the greatest possible number of bulbs per row and no bulbs left over.

   (a)

   Express 90 and 126 as products of their prime factors.

   [3 marks]

   (b)

   Find the HCF of 90 and 126 using prime factors, and hence find the total number of rows needed.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   Three warning lights flash at intervals of 12 seconds, 15 seconds and 20 seconds respectively. They all flash together at exactly 9:00:00 am.

   (a)

   Express 12, 15 and 20 as products of their prime factors.

   [4 marks]

   (b)

   Find the LCM of 12, 15 and 20, and hence find the next time after 9:00:00 am that all three lights flash together.

   [4 marks]

   (c)

   A fourth light is added that flashes every 8 seconds. Find the new LCM of all four intervals (12, 15, 20, 8) and state, in minutes and seconds, how long after 9:00:00 am all four lights will next flash together.

   [5 marks]

   Total for question 4: 13 marks

End of questions