Dana 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 Dana can make? How many candy canes will be in each bag? How many cookies will be in each bag?

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Mathematics

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23 August, 20:24

Dana 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 Dana can make? How many candy canes will be in each bag? How many cookies will be in each bag?

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Brady Pennington · Answer 1

15 gift bags

5 candy canes

3 cookies

Step-by-step explanation:

The greatest number of gift bags will be the greatest common factor (GCF) of 75 and 45.

First, write the prime factorization of each:

45 = 3² * 5

75 = 3 * 5²

The GCF is the product of each factor with the lowest exponent.

GCF = 3 * 5

GCF = 15

The greatest number of gift bags is 15. Each gift bag will have 5 candy canes and 3 cookies.