One.
Only 1 rectangle can be built with a Prime number of square tiles.
If you can only make one rectangle, your number's prime. If you can make more than one, it's composite.
If the tiles cannot be arranged into a rectangle or square it is a prime number.
30: 1x30, 2x15, 3x10, 5x6 24: 1x24, 2x12, 3x8, 4x6 36: 1x36, 2x18, 3x12, 4x9 (6x6 is not a rectangle). 17: 1x17
One.
1
One.
Only 1 rectangle can be built with a Prime number of square tiles.
The number of rectangles you can build with a prime number of tiles depends on many factors such as shape, size, and uniformity of the tiles.
The answer depends on the number of tiles.
If you can only make one rectangle, your number's prime. If you can make more than one, it's composite.
If the tiles cannot be arranged into a rectangle or square it is a prime number.
80
30: 1x30, 2x15, 3x10, 5x6 24: 1x24, 2x12, 3x8, 4x6 36: 1x36, 2x18, 3x12, 4x9 (6x6 is not a rectangle). 17: 1x17
One
Given P = Prime number then you can build (P-1)/2 number of rectangles given any prime number. All prime numbers are odd and you would need two squares to make a rectangle. Given that you need two squares to build a rectangle, you divide your prime number by two to get the number of "pairs" of squares and thus the number of rectangles you can build. Since the number 2 does not divide evenly into an odd number - all prime numbers are odd - then you either subtract one from the prime number before dividing or discard the remainder if you choose not to subtract one before dividing.