R = the square root of P.
If P = H * L, either H = L = the square root of P, or H or L is < R and the other is > R.
If both were > R, then their product would be greater then P, and if both were less than R, their product would be less than P.
There are no integers less than R (the square root of P) that divide evenly into P.
There are no integers greater than R that divide evenly into P.
Assume:H is an integer > R and that H divides evenly into.
Then: Define Las L = P / H.
L is an integer, since L = P / H and H divides evenly into P