Zero is an even number as it is divisible by 2 with no remainder. It is either negative nor positive. The number 0 may or may not be considered a natural number, but it is an integer.

0 is a palindromic number.

0 is a pronic number:

0 is the identity element with respect to addition:

0 is the absorbent element with respect to multiplication:

Also,

We cannot divide by 0 as it has no multiplicative inverse.

The expression

appears sometimes when we attempt to determine the limit of an expression of the form

This is one of the seven indeterminate forms. 

The other indeterminate forms that includes 0 are:

By definition, the factorial of 0 is 1: