Is Zero An Odd Or Even Number?

Zero is a weird number. Well, not weird as in “abundant but not semiperfect” – let’s just say it’s “unusual”. Okay, not unusual like “its largest prime factor is strictly greater than its square root” – maybe we should just describe it as “odd”. Or should we?

Because of its unique place on the number line, people can sometimes get confused about whether zero is an odd or an even number. It’s understandable – zero does do some pretty unexpected things, mathematically speaking. For example, if we tell you that this

means “multiply this number by every single integer below it until you get to 1” – for example, 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800 – then you probably wouldn’t believe us if we said that 0! = 1. But it’s true – as is the equally nonsensical-seeming statement that 0⁰ = 1 … just so long as we’re not dealing with analysis, where the answer is “sorry, but you just broke the universe”.

Even the more simple interactions involving zero seem to be vaguely bananas. You can take any number, as big as you like – thirty-two bajillion, six hundred and three, for example – multiply it by zero, and the whole thing disappears. Divide it by zero, and we’re in universe-breaking territory again. Frankly, you can see why humanity put off dealing with it for as long as we did.

With all this weirdness around multiplying and dividing and zero, it’s no surprise people can get confused over whether the number is odd or even. Reminder: a number is even if it can be divided by two, and odd if dividing by two leaves a remainder one. You can think of it geometrically to see the difference:

So, let’s clear this up: zero is an even number. Perhaps the easiest way to show this is via the diagram above: draw zero blocks – there’s no remainder one, is there? Therefore, it must be even.

But we can do it by definition, too. While you can’t divide any number by zero, you certainly can divide zero by any other number – the answer is simply zero again. To use the kind of phrasing we hear in school, “how many apples does each person get if you start out with zero apples?”

To find out whether zero is even, then, we just need to ask this: is it a multiple of two? And the answer is yes: 0 = 0 × 2.

In summary: zero may be… an idiosyncratic number. But it certainly is not odd.

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