Question

Dylan is planting flower boxes to decorate the school entrance. He has 64 marigolds and 72 periwinkles. Each flower box must contain both flowers. He puts the same number of marigolds in each flower box, and the same number of periwinkles in each flower box. What is the maximum number of flower boxes Dylan can plant and how many marigolds and periwinkles will each flower box have?

Answer 1

Dylan can plant maximum 8 plants.

Number of marigolds in each flower box
`=8`

Number of periwinkles in each flower box
`=9`

Explanation:

Number of marigolds = 64

Number of periwinkles = 72

To find the maximum number of flower boxes Dylan can plant, find H.C.F of 64 and 72.

`64=2^6\\72=2^3\,\,3^2`

So,

H.C.F(64, 72) =
`2^3=8`

That is Dylan can plant maximum 8 plants.

Number of marigolds in each flower box =
`(64)/(8)=8`

Number of periwinkles in each flower box =
`(72)/(8)=9`