What are the divisors of 0?

2 Answers
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 #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.

Mar 11, 2018

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