Odd Numbers and Their Properties

In ancient Greek, the numbers that could not be arranged in two rows were considered odd. However, this concept has changed over the centuries. You can take any multiple of 2. You would come to know that these numbers can be arranged in pairs of 2. And all the integers except the multiple of 2 are odd numbers. In mathematics, we categorised numbers as odd and even numbers. We have to check whether the number is divisible by two or not. If the number is divisible by 2, then it is an even number, and if it is not divisible by 2, it is an odd number. 

Properties of Odd numbers

If you do some arithmetic operations on the odd numbers, can you come to any common conclusion and apply it to all odd numbers? The answer is yes, you can. There are some simple properties of odd numbers that apply to any odd number that you can think of. Let’s discuss it in detail with examples. Given below is the list of all the properties that will be applicable for an odd number: 

1. Additional Property: When we add two different or the same odd numbers, the outcome becomes an even number. For example:  5(odd ) + 3(odd) = 8(even).

So, based on the above experiment, it is clear that the sum of two different or same odd numbers is an even number.

2. Subtraction Property: The outcomes become an even number when we subtract two different or the same odd numbers. For example: 9(odd) – 5(odd) = 4(even).

So, based on the above experiment, it is clear that the subtraction of the two different or same odd numbers is an even number. 

3. Multiplication Property: When we multiply two different or the same odd numbers, the outcomes become an odd number. For example 5(odd) × 7(odd) = 35(odd).

So, based on the above experiment, it is clear that the multiplication of the two different or same odd numbers is an odd number.

4. Division Property: When we divide two different or same odd numbers, the outcome becomes an odd number. For example 63(odd) ÷ 9(odd) = 7(Odd).So, based on the above experiment, it is clear that the division of the two different or same odd numbers is an odd number.

Types of Odd Numbers 

I hope it is clear what are odd numbers? We have learned that odd numbers are those numbers that are not divisible by 2, so it seems like a vast set of numbers. And these vast numbers are categorised into two factors which you can see below: 

1. Consecutive Odd Numbers

Consecutive odd Numbers are those odd numbers that follow each other, and the difference between them is 2. For example, suppose n is an odd number, then the numbers n and n+2 are considered consecutive odd numbers. For example, 3, 5, 7, 9 and 37, 39, 41, 43, etc. The list is endless.

2. Composite Odd Numbers 

The odd whole numbers, which are not whole prime numbers (A number with precisely two factors are called prime numbers), are known as odd composite numbers. Simply, the odd number with multiple factors is an odd composite number. The odd composite numbers from 1 to 100 are 9, 15, 21, 25,………………………….95, 99.

Tips and Tricks for Odd numbers 

There are a few tricks and tips on odd numbers based on which you would have more clarity and deep understanding of odd numbers. Let’s discuss some of them in detail: 

• The easiest method to find out whether a number is odd or even is to divide it by 2; if the number is fully divisible by 2, it’s an even number, and if the number is not divisible by 2, the number is odd.

Odd numbers can not be arranged in pairs. You can also use the equation for odd numbers to check or find odd numbers, i.e. K = 2n ±1,  where K can be any natural number and n is a whole number. We will furthermore learn the properties and types of odd numbers in detail.

Conclusion

The concept of the numbers is vast, and we were specific at the odd numbers in the above article. We learned the definition, all properties, types of odd numbers in a very simple and detailed format. Our efforts are to work on the root and make the lesson simple so that each student can understand all the concepts needed for them to become a topper. We hope you learned a lot with the help of this article on odd numbers, and if you have any queries regarding odd numbers, just ping us in the comment box, we will come back to you as soon as possible.