# factors of 12

- Author:
- Michal J Wallace

If you take all the prime factors of a whole number N, and list out every possible way of breaking them into 2 groups, then you will have pairs representing the far corners of every rectangle with area N. Since each one of these points follows the rule x*y=n, they fall along the hyperbola with that equation.
So: if you had a table with the Cartesian coordinate system drawn on it, and a conic lamp, you could position the lamp over the table so that it lights up one half of this hyperbola. Then you could look along the edge of the light and see if it intersects the grid or not. If it only intersects the grid at (1,n) and (n,1), this number is prime. (Of course, in practice the light would often come so close to an intersection that it would be really hard to tell.)