Amita wants to make a mold for a candle. She wants the shape of the candle to be a rectangular prism with a volume of exactly 28 cubic centimeters. She wants the sides to be in whole centimeters. How many different molds can she make?

Have you attempted to write out combinations of integers that multiply to 28? Start by finding the prime factors of 28, and see how many combinations of these numbers plus the number 1 you can make so that you have three numbers that multiply to 28. Ignore duplicate answers (i.e the same set of numbers in a different order don't count).