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
Why 0 Is Even Explained Mathematically
Image: Shutterstock / Built In
Brand Studio Logo

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.

More on StatisticsPigeonhole Principle Explained

 

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.

Mathematical proof for why 0 is not odd.
Mathematical proof for why 0 is not odd. | Image: Maike Elisa Müller
A tutorial on why 0 is even. | Video: Numberphile

More on StatisticsHow to Prove Causation

 

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?

Hiring Now
Outdoorsy
Insurance • Sharing Economy • Software • Travel
SHARE