Elijah bought bottles of mango syrup, lemon syrup and kiwi syrup of 400 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 mango syrup, lemon syrup and kiwi syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
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 400 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 mango syrup
= 400 ÷ 50
= 8

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

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

Elijah would have 8 cups of mango syrup, 3 cups of lemon syrup, 9 cups of kiwi syrup

Answer(s): (a) 50 mℓ; (b) 8, 3, 9