How many rectangles can you build with a prime number square tiles?

Answer 1

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.