 # Odd and Even Numbers – Definition, Properties, Examples | How to Check if a Number is Even or Odd?

In this article, we will discuss in detail the classification of real numbers namely even and odd numbers. Check out the Definition of Even and Odd Numbers, Set Representation, Flow Chart, Properties, etc. Refer to the further modules to identify even and odd numbers, list of even and odd numbers between 1 to 100. Be well versed with these details and apply this knowledge to your related mathematical concepts learning.

## Definition of Even and Odd Numbers

In general even and odd numbers are defined as follows
Even Numbers: Numbers that are divisible by 2 and leaves a remainder 0 or no remainder are called Even Numbers.
Odd Numbers: Numbers that are not divisible by 2 or leaves a remainder 1 when divided by 2 are called Odd Numbers.

### Even and Odd Numbers Set Representation

Sets Representation of Even and Odd Numbers can be denoted using the

• Even = {2k : k ϵ Z}
• Odd = {2k + 1 : k ϵ Z}

Even Number is an integer represented in the form of n= 2k and Odd Number is an integer represented in the form of n = 2k+1. This is applicable only for integers.

### Properties of Even and Odd Numbers

Below is the list of some of the properties of Even and Odd Numbers. They are along the lines

• The Sum of Two Even Numbers is always an Even Number.
• Sum of Two Odd Numbers is also an Odd Number.
• The Sum of an Even and Odd Number is an Odd Number.
• Even is completely divisible by 2 and leaves a remainder 0.
• Odd Number will not be completely divisible by 2 and leaves a remainder 1.
• Even Number ends with digits 0, 2, 4, 6, 8 whereas Odd Numbers end with digits 1, 3, 5, 7, 9.

### How to Check if a Number is Even or Odd? | Identifying Even and Odd Numbers

We know that Even Numbers ends with the digits 0, 2, 4, 6, 8 and odd numbers end with digits 1, 3, 5, 7, 9, etc. So, in order to determine whether a number is even or odd, you just need to comprehend the digit in one’s place. This single number helps to tell whether the entire number is even or not without actually performing division and looking at the remainder.

Example: 23456 this is an even number as the last digit is 6.
1231 is an odd number as the last digit is 1.

### Odd and Even Numbers Flowchart

Below is the flowchart for Odd and Even Numbers. You can easily understand the differences between even and odd numbers and their working by checking out the below pictorial representation. ### Even and Odd Numbers

If we can divide digits into two groups having an equal number of elements in each then the number is an even number. In the case of odd numbers, this is not possible and we will have a remainder 1. Even numbers end in 2, 4, 6, 8, and 0, irrespective of the preceding digits they have.

Odd Numbers ends in 1,3,5,7,9, independent of the preceding digits they have.

### List of Even and Odd Numbers Between 100

Check out the below image to know the list of Even And Odd Numbers Between 1 and 100. We have represented the Even Numbers marked in Red and Odd Numbers marked in Black for easy identification. Take a Printout of this handy image for free and try to learn the Even and Odd Numbers List between 1 to 100 in no time. ### How to Teach Even and Odd Numbers? | Even and Odd Numbers Songs for Kids

Help your kids learn about the Even and Odd Numbers in a fun and engaging way by making use of the below provided Elementary Math Songs for Even and Odd Numbers. Sing along these songs on Odd and Even Numbers and learn to identify them, properties, etc. easily.

Even number song (elementary math)
Split em up,
Evens split,
Down the middle,
Split em up,
Evens split,
Say this rhyme…
Even numbers split,
Right down the middle,
Half and half,
Make even numbers
Every time

0, 2-4-6-8
0, 2-4-6-8
Say this rhyme,
If ANY number ends,
With one of those digits,
Then that number’s even,
Every time…

Odd number song (elementary math)
Odd numbers
Odd numbers
Can’t be beat,
Those 5 digits,
Are so sweet…
Hey odd numbers!
Go odd numbers!
1,3,5,7,9
The only odd digits,
All the time!
Hey odd numbers!
Go odd numbers!
1,3,5,7,9
The only odd digits,
All the time!
Hey odd numbers!
Go odd numbers!

Odd and Even Number Song
A song about Odd and Even Numbers
If a number is even you can break it into two equal groups.
If a number is odd then you can’t
Even numbers all end with 0, 2, 4, 6, or 8
And the numbers that are odd, well they don’t.

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