Question

Mary has 50 earring boxes. The boxes measure 1 inch on each side. How many rectangular prisms, each with a different-sized base, could Mary make by stacking all of the earring boxes?

Answer 1

Answer: 3.

The volume for all the boxes is 50in³ because 1 * 1 * 1 * 50 = 50.
Next, let's prime factorize 50 so that (using multiplication) we can find all the different bases.
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1

2 * 5² * 1

height x length x width

1 x 5 x 10
1 x 2 x 25
1 x 1 x 50