A question that my students frequently ask me is: “Is 0 even or odd or both?”

To answer this question, we first need to define what “even” means:

An even number is a number `n`

which can be written as `n=2⋅k`

for a whole number `k`

. That means if we divide an even number by two, there is no remainder left.

## Is 0 Even?

An even number in mathematics is a number that can be written as `n=2⋅k`

for a whole number `k`

. If `k=0`

, the equation `0=2⋅k`

remains accurate. This makes 0 an even number.

Can we write `0=2⋅k`

for some `k`

? Yep, we can if we choose `k=0`

.

That means that zero is even.

## Is 0 Also Odd?

Again, we first need to define what “odd” means. The common definition is very similar to the definition of even.

An odd number is a number n which can be written as `n=2⋅k+1`

for a whole number `k`

.

Can we write `0=2⋅k+1`

for some whole number k?** **Nope. We can’t because solving this equation for `k `

yields `k=-1/2,`

which is not a whole number.

## Is 0 Even? Answered.

Alright, the proof is done. Zero is even and only even. And it isn’t *even* (pun intended) too difficult, is it?