The skinny one. A Prime number only has two factors (one rectangle). The factors are one and the number itself.
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Only 1 rectangle can be built with a Prime number of square tiles.
If the tiles cannot be arranged into a rectangle or square it is a prime number.
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.
810
The length ad the width is 16 and 3 because 16 times 3 equals 48 and 16 plus 3 equals 19 which is a prime number because its only factors are 1 and itself