Xavier bought bottles of pomegranate syrup, kiwi syrup and mango syrup of 350 mℓ, 450 mℓ and 150 mℓ respectively. He counted to pour them into smaller cups of equal amount with no leftover.

1. What was the largest possible amount of syrup in each cup?
2. How many cups of syrup of pomegranate syrup, kiwi syrup and mango syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 350: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Highest common factor of 350 mℓ, 450 mℓ and 150 mℓ = 50 mℓ

So, 50 mℓ is the largest possible amount of syrup in each cup.

(b)
Number of cups of pomegranate syrup
= 350 ÷ 50
= 7

Number of cups of kiwi syrup
= 450 ÷ 50
= 9

Number of cups of mango syrup
= 150 ÷ 50
= 3

Xavier would have 7 cups of pomegranate syrup, 9 cups of kiwi syrup, 3 cups of mango syrup

Answer(s): (a) 50 mℓ; (b) 7, 9, 3