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Is Zero Odd or Even?

Date: 06/17/98 at 22:21:48
From: wendy
Subject: Zero

Is zero odd or even?  My 4th grade students are not satisfied with any 
explanation I can offer. Zero after any other number is even because 
it can be divided by 2. It holds an even place in the number line. Is 
it just special the way that 1 is neither prime nor composite?

Date: 06/19/98 at 14:43:11
From: Doctor Mateo
Subject: Re: Zero

Hello Wendy,

You are right. Zero is an even number. An even number is a number that 
is exactly divisible by 2. That means that when you divide by two the 
remainder is zero. You may want to review the multiplication facts
for 2:

 2 x 0 =
 2 x 1 =
 2 x 2 =
 2 x 3 =
 and so on.

After writing these number facts out or reviewing them with the class 
you can ask them about patterns and eventually tell them that this is 
how they can create a list of even numbers.  

Then have them divide several numbers by 2 (including 0) and let them 
see a second way to conclude that a number is even (the remainder of 
the evens is 0 and the remainder of the odds is 1).

Later when the number system is expanded to include the set of 
integers, they will be able to carry the concept over without much 

For more on integers, see the Dr. Math FAQ:

"Integers are the whole numbers, negative whole numbers, and zero... 
The terms even and odd only apply to integers; 2.5 is neither even nor 
odd. Zero, on the other hand, is even since it is 2 times some 
integer: it's 2 times 0."   

Hope this helps. 

-Doctors Mateo and Sarah,  The Math Forum   
Associated Topics:
Elementary Number Sense/About Numbers
Middle School Number Sense/About Numbers

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