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

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Apr 3, 2017

$4$

#### 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 $1 , 2 , 4 , 8 \mathmr{and} 16$.

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 :
$1 \times 1 \times 16$
$1 \times 2 \times 8$
$1 \times 4 \times 4$
$2 \times 2 \times 4$

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

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