Rosa has 16 unit cubes. How many different rectangular prisms can she build with the cubes?

1 Answer
Apr 3, 2017

Answer:

#4#

Explanation:

Since the rectangular prism is formed by the unit cubes, each dimension of the prism must be a whole number of cubes.

Given that Rosa has #16# unit cubes, so we need to find the total number of different combinations of three whole number that have a product of #16#.

To find these combinations, look at the factors of #16#.
They are #1,2,4,8 and 16#.

Pick any two of these factors and determine if there is a third value from this list so that the product of the three factors is #16#

There are #4# combinations that will work :
#1xx1xx16#
#1xx2xx8#
#1xx4xx4#
#2xx2xx4#

Hence, Rosa can build 4 different rectangular prisms with 16 unit cubes.

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