The odd and even numbers are notable and interesting precisely because they are alternative. The counting numbers $1, 2, 3, 4, 5, 6...$ go odd, even, odd, even, odd, even.... In this section we will be learning more about odd numbers and its properties.

A whole number is called odd if it is not exactly divisible by $2$. whole number $1,3,5,7,9$.....are odd numbers, because none is divisible by 2. In the system of whole numbers, odd number and even number occur alternatively.

Two numbers are called consecutive numbers if they differ by one when written in an ascending order. The difference between two consecutive odd number is 2.
In very simple mathematical terms we define ODD Numbers  as " All Integers which are not divisible by 2 ",  i.e. an Integer of the form  "$n = 2k + 1$"  where k is an integer. An Odd number leaves a remainder $1$ when divided by 2.
Properties of odd number:
 
1. Odd number + Odd number = Even number
    Example: $11 + 13$ = $24$
   
2. Odd number + Even number = Odd number
    Example: $11 + 14$ = $25$
 
3. Odd number - Odd number = Even number
    Example: $27 - 13$ = $14$
   
4. Even number - Odd number = Odd number
    Example: $20 + 3$ = $17$
   
5. Odd number $\times$ Odd number = Odd number
    Example: $11 \times 13$ = $143$
   
6. Odd number $\times$ Even number = Even number
    Example: $11 + 20$ = $220$
The following are the list of odd numbers between 1 and 100

Odd Numbers

ODD numbers always ends with one of these digits.......
$1, 3, 5, 7$ or $9$
The following are the examples of odd numbers

Solved Examples

Question 1: Find all the odd number between 50 and 76
Solution:
 
The odd numbers between 50 and 76 are

51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75
 

Question 2: Find out whether the given number is even or not?
    123, 846, 147, 19, 100
Solution:
 
a) 123
The last number is 3, so the number is odd.
b) 846
The last number is 6, so the number is not odd.
c) 147
The last number is 7, so the number is odd.
d) 19
The last number is 9, so the number is odd.
e) 100
The last number is 0, so the given number is even.