Fabian bought bottles of pear syrup, mango syrup and mangosteen syrup of 500 mℓ, 150 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 pear syrup, mango syrup and mangosteen syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
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 500 mℓ, 150 mℓ and 450 mℓ = 50 mℓ

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

(b)
Number of cups of pear syrup
= 500 ÷ 50
= 10

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

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

Fabian would have 10 cups of pear syrup, 3 cups of mango syrup, 9 cups of mangosteen syrup

Answer(s): (a) 50 mℓ; (b) 10, 3, 9