Bryan bought bottles of chikoo syrup, dragonfruit syrup and mango syrup of 200 mℓ, 450 mℓ and 400 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 chikoo syrup, dragonfruit syrup and mango syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Factors of 400: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

Highest common factor of 200 mℓ, 450 mℓ and 400 mℓ = 50 mℓ

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

(b)
Number of cups of chikoo syrup
= 200 ÷ 50
= 4

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

Number of cups of mango syrup
= 400 ÷ 50
= 8

Bryan would have 4 cups of chikoo syrup, 9 cups of dragonfruit syrup, 8 cups of mango syrup

Answer(s): (a) 50 mℓ; (b) 4, 9, 8