Question

Suzanne will use orange and blue beads to make bracelets. She will use the same number of orange beads on each bracelet and the same number of blue beads on each bracelet. She has 72 orange beads and 78 blue beads. What is the greatest number of bracelets that she can make that will have the greatest number of orange beads and blue beads?

Answer 1

6 bracelets with 12 orange beads and 13 blue beads in each.

Explanation:

Suzanne has 72 orange beads and 78 blue beads. She will use the same number of orange beads on each bracelet and the same number of blue beads on each bracelet.

Factor these two numbers:

`72=2\cdot 36=2\cdot 2\cdot 18=2\cdot 2\cdot 2\cdot 9=2\cdot 2\cdot 2\cdot 3\cdot 3\\ \\78=2\cdot 39=2\cdot 3\cdot 13`

Find GCF(72,78):

`GCF(72,78)=2\cdot 3=6`

Since

`72=6\cdot 12\\ \\78=6\cdot 13,`

Suzzanne can make maximum 6 bracelets with 12 orange beads and 13 blue beads in each.