A bakery packages cookies in two sizes of boxes, one with 18 cookies and the other with 24 cookies. A small number of cookies are to be wrapped in cellophane before they are placed in a box. To save money, the bakery will use the same size cellophane packages for each box.
How many cookies should the bakery place in each cellophane package to maximize the number of cookies in each package?
(We are learning about factors and greatest common factors if this helps you a bit.)
factors of 18 = 1, 18, 2, 9, 3, 6
factors of 24 = 1, 24, 2, 12, 3, 8, 4, 6
What is the largest number that is a factor of both 18 and 24?
Right.
To maximize the number of cookies in each cellophane package, we need to find the greatest common factor (GCF) of the two box sizes. The GCF is the largest number that divides both 18 and 24 evenly.
To find the GCF, we can start by listing the factors of both 18 and 24:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
From this list, we can see that the common factors of 18 and 24 are 1, 2, 3, and 6. However, we need to find the greatest common factor.
The GCF of 18 and 24 is 6, because it is the largest number that divides both 18 and 24 evenly.
Therefore, the bakery should place 6 cookies in each cellophane package to maximize the number of cookies in each package.