Tom bought bottles of starfruit syrup, mango syrup and pomegranate syrup of 450 mℓ, 300 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 starfruit syrup, mango syrup and pomegranate syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Highest common factor of 450 mℓ, 300 mℓ and 150 mℓ = 150 mℓ

So, 150 mℓ is the largest possible amount of syrup in each cup.

(b)
Number of cups of starfruit syrup
= 450 ÷ 150
= 3

Number of cups of mango syrup
= 300 ÷ 150
= 2

Number of cups of pomegranate syrup
= 150 ÷ 150
= 1

Tom would have 3 cups of starfruit syrup, 2 cups of mango syrup, 1 cups of pomegranate syrup

Answer(s): (a) 150 mℓ; (b) 3, 2, 1