Factors of zero? How many integer factors of 0 are there, and what are they?
I'm just curious, but what counts as a factor of 0? My guess is that there are an infinite number of factors of 0, but is there a proof?

The statement

$a$ is a factor of $b$

means

$b=ka$ for some integer $k$.

Take $b=0$: then no matter what $a$ is, the equation $0=ka$ is always true for some value of $k$, namely, $k=0$.  So every integer is a factor of $0$.

This is an excellent example of the importance of using definitions precisely.  Some people think that a factor of $b$ means


$b$ divided by any integer "which goes exactly",

for example, the factors of $10$ are $10/1$, $10/(-2)$, $10/5$ etc.  This would give the factors of $0$ as being $0/1$, $0/2$ etc, in other words, $0$ only, which is not correct.
