Cody bought bottles of persimmon syrup, passion fruit syrup and starfruit syrup of 300 mℓ, 250 mℓ and 450 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 persimmon syrup, passion fruit syrup and starfruit syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450

Highest common factor of 300 mℓ, 250 mℓ and 450 mℓ = 50 mℓ

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

(b)
Number of cups of persimmon syrup
= 300 ÷ 50
= 6

Number of cups of passion fruit syrup
= 250 ÷ 50
= 5

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

Cody would have 6 cups of persimmon syrup, 5 cups of passion fruit syrup, 9 cups of starfruit syrup

Answer(s): (a) 50 mℓ; (b) 6, 5, 9