# Why 0 Is Even Explained Mathematically

Zero is an even number because it can be divided by two without producing a remainder. Learn how to prove 0 is even and why it isn’t also an odd number.

Published on Feb. 06, 2024
Image: Shutterstock / Built In

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.

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## 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.

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