# What are the divisors of 0?

Mar 11, 2018

All non-zero numbers are divisors of $0$. $0$ may also be counted as divisor, depending on whose definition of divisor you use.

#### Explanation:

This answer assumes the following definition of divisor:

For integers $m , n$ we say that $m$ is a divisor of $n$ and write $m | n$ if and only if there is some integer $k$ such that $k m = n$.

If $n$ is any number then $n \times 0 = 0$.

So $n$ is a divisor of $0$.

Note that there are several different definitions of divisor in use. Some specify that $m | n$ if and only if $\frac{n}{m}$ is an integer - i.e. has no remainder. Under that definition $0$ would not be counted as a divisor of $0$, since $\frac{0}{0}$ is undefined.

Mar 11, 2018

Any and every number can be divided into $0$ EXCEPT $0$