Question

Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?

Answer 1

You need to find the greatest common factor of 30 and 48.

First find the prime factorizations of 30 and 48.

30/2 = 15
15/3 = 5
5/5 = 1

48/2 = 24
24/2 = 12
12/2 = 6
6/2 = 3
3/3 = 1

The prime factorizations are:
30 = 2 * 3 * 5
48 = 2^4 * 3

To find the GCF, you need the product of the common factors with the lower exponent.

Both 30 and 48 have 2 as a factor. 30 has 2 and 48 has 2^4. Pick the one with the lower exponent: 2.

Both 30 and 48 have 3 as a common factor. Pick 3.

GCF = 2 * 3 = 6

She needs 6 containers.

Answer 2

You find the gcf/ greatest common factor of both numbers which is 6, so 6 plastic containers.