A math line interpretation From the text of the question posed here: "How many whole numbers less than 2010 have exactly three factors?" this statement is made:

If there is no fourth factor, then that third factor must be the
  square root of the number. Furthermore, that third factor must be a
  prime, or there would be more factors.

I don't understand this. Can you explain please. 

The number must be the square of a prime to have exactly three factors.
The number itself, $n$, and $1$ are two of them.  This leaves one more factor, which itself must not have any other factors besides $1$ and itself, which are counted already.  Hence this last factor must be a prime, $p$.
The fact that there are no other factors besides $1, p, n$ means that the $n = p^2$.  The value of $n$ cannot be some higher power of $p$ because then $p^2$ would be a separate (fourth) factor.
