Tom bought bottles of lemon syrup, pomegranate syrup and mango syrup of 450 mℓ, 500 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 lemon syrup, pomegranate syrup and mango 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 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
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 450 mℓ, 500 mℓ and 300 mℓ = 50 mℓ

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

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

Number of cups of pomegranate syrup
= 500 ÷ 50
= 10

Number of cups of mango syrup
= 300 ÷ 50
= 6

Tom would have 9 cups of lemon syrup, 10 cups of pomegranate syrup, 6 cups of mango syrup

Answer(s): (a) 50 mℓ; (b) 9, 10, 6