Albert bought bottles of kiwi syrup, dragonfruit syrup and mango syrup of 300 mℓ, 250 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 kiwi syrup, dragonfruit syrup and mango syrup would he have respectively? Give your answers in numbers (Eg 1, 2, 3)

(a)
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

Highest common factor of 300 mℓ, 250 mℓ and 200 mℓ = 50 mℓ

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

(b)
Number of cups of kiwi syrup
= 300 ÷ 50
= 6

Number of cups of dragonfruit syrup
= 250 ÷ 50
= 5

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

Albert would have 6 cups of kiwi syrup, 5 cups of dragonfruit syrup, 4 cups of mango syrup

Answer(s): (a) 50 mℓ; (b) 6, 5, 4