Question

A florist is making identical bouquets using 72 red roses, 60 pink roses, and 48 yellow roses. What is the greatest number of bouquets that the florist can make if no roses are left over

Answer 1

we know that

To find the number of bouquets we can make, we find the GCF (greatest common factor) of the three numbers, 72, 60 and 48. To do this, we find the prime factorization of each

`72=2^(3)*3^(2)`

`60=2^(2)*3*5`

`48=2^(4)*3`

The GCF is equal to--------->
`2^(2)*3`------->
`12`bouquets.

72/12 = 6; this means we use 6 red roses in each bouquet.

60/12 = 5; this means we use 5 pink roses in each bouquet.

48/12 = 4; this means we use 4 yellow roses in each bouquet.

therefore

the answer is

the greatest number of bouquets that the florist can make is 12 bouquets