Aliyah has 75 candy canes and 45 holiday cookies. She wants to divide them into gift bags, so that each bag has an equal number of candy canes and each bag has the same number of cookies as all the other bags. What is the greatest number of gift bags that Aliyah can make? How many candy canes will be in each bag? How many cookies will be in each bag?

1) 15 gift bags 2) 3 holiday cookies

Explanation:

1) Find the greatest number that divides exactly both 75 (candy canes) and 45 (holiday cookies).

That is, find the GCF (greatest common factor) of 75 and 45.

45 = 3² * 5 75 = 3 * 5² GCF = common factors each raised to its least exponent: 3*5 = 15

Then, the greatest number of gift bags, so that each bag has an equal number of candy canes and same number of cookies that Aliyah can make is 15.

2) How many cookies will be in each bag?

To find the number of cookies that will be in each bag, you divide the number of holiday cookies by the number of gift bags:

45 holiday cookies / 15 gift bags = 3 holiday cookies per bag.

Thus, each bag will contain 3 holiday cookies.