Asher bought bottles of mango syrup, guava syrup and grapefruit syrup of 450 mℓ, 150 mℓ and 200 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 mango syrup, guava syrup and grapefruit 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 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

Highest common factor of 450 mℓ, 150 mℓ and 200 mℓ = 50 mℓ

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

(b)
Number of cups of mango syrup
= 450 ÷ 50
= 9

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

Number of cups of grapefruit syrup
= 200 ÷ 50
= 4

Asher would have 9 cups of mango syrup, 3 cups of guava syrup, 4 cups of grapefruit syrup

Answer(s): (a) 50 mℓ; (b) 9, 3, 4