Odd Numbers and its Properties

odd numbers

Odd numbers are the numbers that cannot be divided by the number two evenly. Also, it can’t be divided into two separate integers evenly. You might have studied odd numbers and their various aspects in your school. Some of the examples of odd numbers are 1, 3, 5, 7, 9, etc. Can you recall some of the properties of the odd numbers? No? In this article, we will try to understand some concepts related to these numbers such as properties of odd numbers, types of odd numbers, some important facts to remember about odd numbers, and much more. Before moving into the types of odd numbers and their properties, let us discuss in brief even numbers too.

Types of Odd Numbers

Broadly, odd numbers can be divided into two categories. Let us discuss them.

  • Consecutive odd numbers: Let us assume that a is an odd number then ‘a’ and ‘a + 2’ are consecutive odd numbers. There are two types of consecutive odd numbers, negative and positive consecutive odd numbers. Let us see some of the related examples of these numbers, 3 and 5 are positive consecutive odd numbers while -5 and -3 are negative consecutive odd numbers respectively.
  • Composite odd numbers: A number that is formed by the multiplication of two smaller positive integers is known as a composite odd number. Some of the examples are, 9, 15, 21, 25, etc. 

Properties of Odd Numbers

Generally, we study about 4 properties of odd numbers. The following points below analyze those four properties. 

  • Adding two Odd numbers: The addition of two odd numbers results in the formation of an even number. Odd number + Odd number = Even number. Let us see an example, let ‘3’ be the odd number, adding it twice gives us 6 which is an even number.
  • Subtraction of two Odd numbers: As mentioned above, the addition of two odd numbers gives us an even number, similarly subtraction of two odd numbers gives us an even number. Odd number – Odd number = Even number. For example, let the two odd numbers be 5 and 3, subtraction of these numbers gives 2, which is an even number. 
  • Multiplication of Odd numbers: This property basically signifies that the multiplication of two odd numbers gives an odd number itself. Odd number * Odd number = Odd number. For example, 3 is an odd number, if we multiply it by an odd number the result will be an odd number. Such as, 3 * 9 = 27. 
  • Division of Odd numbers: This property is similar to the property mentioned above(multiplication of two odd numbers). If we divide two odd numbers, the result will be an odd number as well. Odd number / Odd number = Odd number. For example, if we divide 27/9 the result will be 3, which is an odd number. 

Even Numbers

Even numbers can be defined as any numbers that can be exactly divided by 2. Even numbers are exactly the opposite of odd numbers. Some of the examples of even numbers are, 2, 4, 6, 8, 10, etc. One of the useful facts to recognize even numbers is that all the even numbers end with the digit, 0, 2, 4, 6, 8. You should note that the smallest positive even natural number is 2. Knowing about even numbers helps us in understanding odd numbers easily since both are mutually exclusive in a set of natural numbers. 

Facts to Remember about Odd Numbers

  1. A number that is not a multiple of two is an odd number. 
  2. If an odd number is divided by 2, there will be a remainder left every time. 
  3. If we go by the number line, the first odd number is 1 which is a positive odd number.

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