The definition I found on most websites was "A natural number $x$ is a factor of a natural number $y$ if $\frac{y}x$ leaves no remainder."
This definition seemed correct until I searched "What are the factors of $\sqrt2$?" The majority of the people seemed to say that the factors of $\sqrt2$ are $1$ and $\sqrt2$. This does not make sense, as $\sqrt2$ is not a whole number, and though we technically can't find its proper value, it's still clear that $\sqrt2$ is a decimal number and therefore it should have no factors.
Also, if $\sqrt2$ is a factor of $\sqrt2$, then $\sqrt2$ should also be an factor of $2$.
So once again, what is the proper definition of a factor in mathematics, and do numbers other than the natural numbers have factors?