Question

What are the divisors of 0?

Answer 1

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 `km = n`.

If `n` is any number then `n xx 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 `n/m` is an integer - i.e. has no remainder. Under that definition `0` would not be counted as a divisor of `0`, since `0/0` is undefined.

Answer 2

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