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.
How long is the rectangle? If the rectangle is only one tile long, then it will take 20 tiles.
Two tiles can only make one rectangle.
No single integer satisfies both requests. 80 is the only integer with exactly 5 factor pairs in that range, but it has two prime factors. 64 and 81 have one prime factor but 4 and 3 factor pairs respectively.
Only 1 rectangle can be built with a Prime number of square tiles.
Assuming that you are asking about a rectangular or square tile, the answer is one--Squares are rectangles with sides of equal lenght.
If you can only make one rectangle, your number's prime. If you can make more than one, it's composite.
80
Using all five tiles, only one rectangle can be made. (1 tile wide by 5 tiles long) Using less than all five tiles, you could make six different rectangles. (squares are technically rectangles too.) The rectangles possible would be: 1 tile wide by 5 tiles long, 1 wide by four long, 1 wide by 3 long, 1 wide by 2 long, 1 wide by 1 long, and 2 wide by 2 long.
1
How long is the rectangle? If the rectangle is only one tile long, then it will take 20 tiles.
You can make 9 triangles but NOT rectangles.
Two tiles can only make one rectangle.
The only ones are (1 x 21) and (3 x 7) .
No single integer satisfies both requests. 80 is the only integer with exactly 5 factor pairs in that range, but it has two prime factors. 64 and 81 have one prime factor but 4 and 3 factor pairs respectively.
5 rectangles means 5 prime numbers in this number 64 = 25 = 64 x 1 = 32 x 2 = 16 x 4 = 8 x 8 : 4 rectangles 96 =24 x 3 = 32 x 3 = 16 x 6 = 8 x 12 = 4 x 24 = 2 x 48 = 1 x 96 : 6 rectangles 72 = 23 x 32 = 72 x1 = 36 x 2 = 18 x 4 = 9 x 8 = 3 x 24 : 5 rectangles!