Short answer: zero is even. It is divisible by 2 with no remainder, and 0 = 2 × 0 fits the definition of an even number exactly.
Research on number cognition has found that people take noticeably longer to classify 0 as even than numbers like 2 or 8, and some students answer “neither”. The hesitation is understandable, because zero feels like “nothing”. But parity is defined by divisibility, and zero passes the test. Here are four independent ways to see it.
Check it yourself
Check zero (or any number)
Yes, it is even
0 is an even number.
- 0 divided by 2 equals 0 with remainder 0.
- Therefore, 0 is even.
Zero is a multiple of 2 (0 = 2 × 0), which is exactly the definition of an even number.
Proof 1: Divide by 2
0 ÷ 2 = 0 with remainder 0. A remainder of 0 is exactly what makes a number even. Compare 1 ÷ 2 = 0 with remainder 1, which is odd.
Proof 2: The definition
An integer n is even if n = 2k for some integer k. With k = 0 we get 2 × 0 = 0, so zero is even. There is no integer k with 2k + 1 = 0, because that would need k = −½, which is not an integer, so zero is not odd.
Proof 3: The number line
Even and odd integers alternate with no gaps. Zero sits between −1 and 1, and both of those are odd, so zero must be even. Shift the line below to see the pattern continue in both directions.
Parity on the number line
- −5odd
- −4even
- −3odd
- −2even
- −1odd
- 0even
- 1odd
- 2even
- 3odd
- 4even
- 5odd
Even and odd alternate with no gaps. Zero sits between −1 and 1, which are both odd, so zero must be even.
Proof 4: The parity rules
We know odd + odd = even, and 1 + (−1) = 0. We also know even − even = even, and 2 − 2 = 0. If zero were odd, these well-established rules would break. They only stay consistent if zero is even.
Why people think zero might be neither
- Zero is neither positive nor negative, and people sometimes carry that “neither” over to parity. Sign and parity are separate properties.
- Counting starts at 1 for young children, so early examples of even numbers are 2, 4, 6 and zero is rarely mentioned.
- “You can’t share nothing”: but splitting zero objects into two equal groups works perfectly, with zero in each group and none left over.
Where the answer matters
Odd–even driving restrictions, used by some cities on high-pollution days, must decide what to do with licence plates ending in 0; the mathematically consistent choice, and the usual one, is to treat them as even. In programming, 0 % 2 === 0 evaluates to true, so loops and alternating patterns that start at index 0 treat the first item as even.
Frequently asked questions
Is 0 an even number or an odd number?
Zero is an even number.
Is zero positive or negative?
Neither. Zero is the boundary between the positive and negative numbers, yet it is still even.
Is zero a natural number?
It depends on the convention. Some textbooks start the natural numbers at 0 and others at 1. Either way, zero is an even integer.
Is 0 a multiple of 2?
Yes. 0 is a multiple of every integer, because 0 = n × 0 for any n.