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How many different rectangular prisms can he build if he uses all the cubes

How many different rectangular prisms can he build if he uses all the cubes-example-1

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It depends on how you count them. If you describe them by their dimensions, lowest one first, you can have
1 x 1 x 18
1 x 2 x 9
1 x 3 x 6
2 x 3 x 3

Of course, these dimensions can be put in any order.
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