3D - 2

All possible dimensions of a 3D box using exactly 40 1-inch cubes.?

I was looking through a problem book today, and found this questiom but couldn't seem to figure it out.

Public Comments

1. 40 = 1 x 1 x 1 x 2 x 2 x 2 x 5 (all prime numbers) So the box could be: 1 x 1 x 40 = 1x40x1 = 40x1x1 1 x 2 x 20 = 2x1x20 = 1x20x2 = 2x20x1 = 20x1x2 = 20x2x1 1 x 4 x 10 = (5 more ways) 1 x 5 x 8 = (5 more ways) 2 x 2 x 10 = (2 more ways) 2 x 4 x 5 = (5 more ways) I think that's all. Six unique ways, plus rotations.