Question

George has baked 48 chocolate chip cookies and 64 snickerdoodlecookies for a bake sale. He wants to make the greatest number ofbags as possible that contain both cookie flavors and have the samenumber of each flavor per bag. How many bags can he make withouthaving any cookies left over?

Answer 1

`16\text{ bags}`

Step-by-step explanation

We want to find the number of bags that he can make without having any leftovers.

To do this, we have to find the highest common factor of the numbers of the two flavors of cookies, i.e. 48 and 64.

To do that, express both numbers as products of their prime factors and pick only the numbers that are common among them:

48 = 2 * 2 * 2 * 2 * 3

64 = 2 * 2 * 2 * 2 * 2 * 2

The boldened numbers are the common ones so, the highest common factor is:

`\begin{gathered} \text{HCF}=2\cdot2\cdot2\cdot2 \\ \text{HCF}=16 \end{gathered}`

Therefore, George can make 16 bags without having any leftovers.