John bought bottles of persimmon syrup, grapefruit syrup and passion fruit syrup of 150 mℓ, 250 mℓ and 300 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, grapefruit syrup and passion fruit syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

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

Highest common factor of 150 mℓ, 250 mℓ and 300 mℓ = 50 mℓ

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

(b)
Number of cups of persimmon syrup
= 150 ÷ 50
= 3

Number of cups of grapefruit syrup
= 250 ÷ 50
= 5

Number of cups of passion fruit syrup
= 300 ÷ 50
= 6

John would have 3 cups of persimmon syrup, 5 cups of grapefruit syrup, 6 cups of passion fruit syrup

Answer(s): (a) 50 mℓ; (b) 3, 5, 6