1. 1
   Two garden centres, Greenfield and Rosewood, are ordering matching sets of plant pots and trays. Greenfield orders 360 identical pots and Rosewood orders 252 identical pots.

   (a)

   Express 360 as a product of prime factors.

   [1 mark]

   • A$2^3 \times 3^2 \times 5$
   • B$2^2 \times 3^3 \times 5$
   • C$2^3 \times 3 \times 5^2$
   • D$2^4 \times 3^2$

   (b)

   Express 252 as a product of prime factors.

   [1 mark]

   • A$2^2 \times 3 \times 7^2$
   • B$2^3 \times 3 \times 7$
   • C$2 \times 3^3 \times 7$
   • D$2^2 \times 3^2 \times 7$

   (c)

   What is the highest common factor (HCF) of 360 and 252?

   [1 mark]

   • A$18$
   • B$36$
   • C$12$
   • D$72$

   Total for question 1: 3 marks

2. 2
   Two lighthouses flash at regular intervals to warn passing ships. Lighthouse A flashes every 18 seconds and Lighthouse B flashes every 24 seconds. Both flash together at exactly 8:00pm.

   (a)

   Two lighthouses flash at regular intervals. Lighthouse A flashes every 18 seconds and Lighthouse B flashes every 24 seconds. Find the lowest common multiple (LCM) of 18 and 24.

   [2 marks]

   (b)

   Using your answer to part (a), find the next time after 8:00pm that both lighthouses flash together.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A ribbon factory has two rolls of ribbon, one of length 84 metres and one of length 126 metres, and wants to cut both into equal-length pieces with none left over, then package the pieces into identical boxes.

   (a)

   Find the HCF of 84 and 126 using prime factorisation.

   [3 marks]

   (b)

   Using the piece length found in part (a), calculate the total number of pieces of ribbon produced from both rolls combined.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A school is organising three coach trips departing from the same car park at 9:00am. Coach P returns every 30 minutes, Coach Q every 45 minutes and Coach R every 60 minutes. The school also wants to split 90 students into equal groups matching a factor of the LCM.

   (a)

   A school is organising three coach trips that depart from the same car park. Coach P returns every 30 minutes, Coach Q returns every 45 minutes and Coach R returns every 60 minutes, all starting together at 9:00am. Find the LCM of 30, 45 and 60 by writing each number as a product of its prime factors.

   [4 marks]

   (b)

   At what time will all three coaches next be back at the car park together?

   [4 marks]

   (c)

   The school wants to divide the students from three year groups, of sizes 90, 108 and 126, into the largest possible number of equal groups so that each group contains a whole number of students from each of the three year groups. Find the HCF of 90, 108 and 126 using prime factorisation, and state the number of groups formed.

   [5 marks]

   Total for question 4: 13 marks

End of questions