Formula for Odd Numbers
Before going to learn the formula for odd numbers, let us recall what are odd numbers. Odd numbers are whole numbers that cannot be exactly divided by 2. For example, numbers 3, 5, 7, 9,.. are odd numbers. The odd numbers formula helps in representing an odd number in general. Let us learn about the formula for odd numbers with a few examples in the end.
What Is the Formula for Odd Numbers?
An odd number can be always expressed as 1 plus an even number. We know that an even number is of the form 2n, where n is a whole number. Thus, the formula for odd numbers can be given as:
Formula for odd numbers = 2n + 1
where n ∈ W (whole numbers)
Let us see the applications of the formula for odd numbers in the following section.
Solved Examples Using Formula for Odd Numbers

Example 1: Check if 23 is an odd number using the formula for odd numbers.
Solution:
To find: Check if 23 is an odd number.
On dividing 23 by 2, it leaves the remainder as 1.
Thus, we conclude that 23 is an odd number.
Answer: 23 is an odd number.

Example 2: Which two digits of the number 6852 must be interchanged to make it an odd number?
Solution:
To find: Digits to be interchanged to make 6852 odd.
An odd number ends in the digit 1, 3, 5, 7, 9.
Therefore, 2 and 5 need to be interchanged to make it odd.
Answer: 2 and 5 need to be interchanged to make it odd.