Question

A florist has 54 white roses, 72 red roses, and 108 pink roses. If he makes the greatest number possible of identical bouquets using all the roses, how many red roses will be in each bouquet?

Answer 1

Find the greatest common factor of each flower:

White roses = 54 = 1, 2 , 3, 6, 9, 18, 27, 54

Red roses = 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Pink roses = 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

The common factors of all three are: 1, 2, 3, 6, 9, 18.

The greatest common factor is 18, so he can make 18 bouquets.

Divide the total red roses by 18:

72 / 18 = 4

There will be 4 red roses in each bouquet.