Sierra baked 80 chocolate chip cookies and 64 sugar cookies. If she would like to equally distribute each type of cookie into containers, what is the greatest number of containers she will need if no cookies are leftover?
Answers
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Answer:
Solution
1, 2, 3, 6, 8, 12, 16, 24, 48.
The number of bags she can make are shown in the table:
Number of CC cookies in each bag 1 2 3 4 6 8 12 16 24 48
Number of bags 48 24 16 12 8 6 4 3 2 1
Since the number of cookies that goes in a bag is a factor of the total number of cookies, all the factors of 48 are listed in the first row of the table. Each column corresponds to a situation where the 48 cookies are divided equally among some bags, and the product of the numbers in each column is 48. The number of bags is also a factor of the total number of cookies.
1, 2, 4, 8, 16, 32, 64.
Number of vanilla wafers in each bag 1 2 4 8 16 32 64
Number of bags 64 32 16 8 4 2 1
Since the number of cookies that goes in a bag is a factor of the total number of cookies, all the factors of 64 are listed in the first row of the table. Each column corresponds to a situation where the 64 cookies are divided equally among some bags, and the product of the numbers in each column is 64. The number of bags is also a factor of the total number of cookies.
1, 2, 4, 8, 16
Since the number of bags must be a factor of both 48 and 64, the common factors of 48 and 64 represent all the possibilities for the number of bags she can make. The table below shows these possibilities along with the number of each kind of cookie that would go in each bag.
Number of bags 1 2 4 8 16
Number of CC cookies in each bag 48 24 12 6 3
Number of vanilla wafers in each bag 64 32 16 8 4
Looking at the table from the third part of this solution, we see that the largest number of bags she can make corresponds to the largest common factor, which is 16 in this case. If there are 16 bags, there will be 3 chocolate chip cookies and 4 vanilla wafers in each.