What numbers of tiles can make 5 rectangles?

Answer 1

Prime numbers raised to the 4th power can make five different rectangles. They can make the following sizes:

1 height by n4 width

n height by n3 width

n2 height by n2 width

n3 height by n width

n4 height by 1 width

24 = 16; rectangles would be 1 x 16, 2 x 8, 4 x 4, 8 x 2, and 16 x 1

34 = 81; rectangles would be 1 x 81, 3 x 27, 9 x 9, 27 x 3, and 81 x 1