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Q: How many rectangle can you build with a prime number of square tiles?

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Only 1 rectangle can be built with a prime number of square tiles.

Because prime numbers only have one factor pair.

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.

If the tiles cannot be arranged into a rectangle or square it is a prime number.

1

Only one.

Only one.

No square number can be a prime number and conversely.

The skinny one. A prime number only has two factors (one rectangle). The factors are one and the number itself.

1 is not a prime number but it is a square number

113 is prime, not square.

prime number

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