Even and Odd Numbers

Even numbers are only divisible by 2, without a remainder. They always have the last digit as 0, 2, 4, 6, or 8. For example, 20, 22, 24, 26, 28, etc.

We mathematically express the set of even numbers as:
{x : x = 2k, where k ∈ W}


Here, 
k: any integer 
W: the whole number set


On the other hand, odd numbers are numbers that cannot be evenly divided by 2. They have the last digit as 1, 3, 5, 7, or 9. For example, 21, 23, 25, 27, 29, etc.

We mathematically express the set of odd numbers as:
{x : x = 2k – 1, where k ∈ Z}

Here, 
k: any integer
Z: the set of integers
 

There are certain differences between even and odd numbers that you should understand. We will now learn the key differences between these sets of numbers:

To find whether a number is even or odd, we follow different methods. Here are a few simple steps to determine them:


Checking the one's place of the given number:
 

• If the given number ends with 2, 4, 6, 8, or 0, it is an even number.
• If the given number ends with 1, 3, 5, 7, or 9, it is an odd number.
   

Equal grouping of numbers:
 

• If you can group numbers into pairs without any left-out pairs, it is an even number.
• If one item remains unpaired, the number is odd.
   

The odd numbers and even numbers have various properties. Here’s a list of them:
 

• The sum of two even numbers is always an even number. 
  For example: 2 + 4 = 6
   
• The sum of an even number and an odd number is always an odd number.
  For example: 12 + 11 = 23
   
• The sum of two odd numbers is always an even number.
  For example: 3 + 5 = 8
   
• The difference between two even numbers is always an even number.
  For example: 24 – 12 = 12
   
• The difference between an even number and an odd number is always an odd number.
  For example: 20 – 9 = 11
   
• The difference between two odd numbers is always an even number.
  For example: 13 – 7 = 6
   
• The product of two even numbers is always an even number.
  For example: 6 × 2 = 12
   
• The product of an even number and an odd number is always an even number.
  For example: 18 × 5 = 90

A visual representation of numbers in a chart helps students easily grasp them. Let’s look at the odd numbers from 1 to 100.

The even numbers from 1 to 100 are listed below:
 

Even numbers and odd numbers are basic mathematical concepts with practical uses that extend beyond math. Let’s look into some of them:
 

• Children use even numbers to equally share anything that can be counted. For example, 14 candies can be shared between two friends without any leftovers.
   
• In many buildings, rooms with odd numbers are on one side, and rooms with even numbers are on the other. This makes it easier to locate rooms.
   
• In theaters or stadiums, seats are often arranged in odd and even order so that the visitors can easily find their seats.
   
• In sports, even numbers are used to form balanced teams, while an odd number may result in one player being left out.
   
• When counting something like money, an odd number tells us that it cannot be completely divided.