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# Odd Numbers

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Numbers starting with 1, 2, 3, 4.…… are called Natural Numbers. Natural numbers are denoted by ‘N’. These numbers are put into different groups. The group may be of Even Numbers, odd numbers, prime numbers or even composite numbers.

Even and odd numbers are the two sides of the same coin, i.e, a number may be either even or odd but cannot be both. No natural number falls out of these two groups. Each natural number will be a member of one of these two groups.

Similarly in the other group, we have Prime and Composite Numbers. It is worth mentioning here that 1 is the only natural number which is neither prime nor composite but there is no natural number which doesn’t fall in either of even or Odd Numbers.

An odd number is a number that is not divisible by 2 which means that the remainder we get on dividing the given number by 2 is 1. If the given number has 1, 3, 5, 7, 9 at its unit place, it is not divisible by 2 and is called an odd number.

We can also make pairs to find if a number is even or not. When we make pairs from the given number, if we cannot make complete pairs and a number is left unpaired then the number is odd.

The general expression for an odd number is,

n = 2k + 1 ; where k = 0, 1, 2, 3,....

For any value of k, the value of n will always be an odd number.

Examples:
1. 21 = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 1. As 1 is left unpaired in this number, it is an odd number.
2. 12 = 2 + 2 + 2 + 2 + 2 + 2. No number is left unpaired, so it is an even number.
3. 7 = 2 + 2 + 2 + 1. As 1 is left unpaired in this number, it is an odd number.
4. 11 = 2 + 2 + 2 + 2 + 2 + 1. As 1 is left unpaired in this number, it is an odd number.