Odd Numbers – Definition, List, Types and Properties
Numbers are of two types even numbers and odd numbers. Odd numbers are the integers that are not divisible by 2. Also, fractions cannot be odd numbers. Vedantu is providing you with a detailed explanation of the concept of odd numbers in a very easy language. The study material is easily available in PDF format and can be downloaded for free from Vedantu.
So, What are Odd Numbers?
Odd numbers are the integers that always leave a remainder when divided by 2. These numbers are the integers with the form n = 2k + 1, where k is an integer. The examples of odd numbers are: -5, -3, -1, 1, 3, 5, 7 and so on. Odd numbers, when divided by 2 always leave a remainder 1, on the contrary even numbers when divided by 2, leave the remainder 0. The smallest positive odd number is 1.
List of Odd Numbers:
There are a total of 50 odd numbers from 1 to 100 and 24 odd numbers from 1 to 50.
Here is a list of odd numbers from -5 to 25:
-5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25.
And the list of the even number is:
-4, -2, 0,2, 4, 6, 8,10, 12, 14, 16, 18, 20, 22, 24.
Types of Odd Numbers:
Composite Odd Numbers: Those composite numbers which cannot be divided by 2 are the composite odd numbers, and all the positive integers that have a factor other than 1 are known as composite numbers. The list of composite odd numbers from 1 to 50 is as follows.
9, 15, 21, 25, 27, 33, 45, 49.
Consecutive Odd Numbers: Consecutive odd numbers follow each other in sequential order. They have a difference of 2 between them.
The consecutive odd numbers from 1 to 10 are:
1, 3, 5, 7, 9.
Properties of Odd Numbers
Odd + Odd = Even
When two odd numbers are added their sum is an even number. For example,
1 + 3 = 4
Here, 1 and 3 are odd numbers but their sum is 4 which is an even number.
Odd – Odd = Even
When an odd number is subtracted from another odd number, the result is an even number. For example,
3 – 1 = 2
7 – 3 = 4
Here 7, 3, and 1 are odd numbers, and the result is an even number.
Odd × Odd = Odd
The product of two odd numbers is always an odd number. For example,
5 × 3 = 15
3 × 3 = 9
Here, 5 and 3 are the odd numbers, and the products too are odd numbers.
Odd/Odd = Odd
The division of two odd numbers always results in an odd number. For example,
3/3 = 1
15/5 = 3
Here the 5, 3, and 15 are the odd numbers and the result of their division result will also be an odd number.
The key features of an odd number are as follows.
- When we divide odd numbers by 2 the remainder should always be 1.
- 1 is the first positive odd number in the number line.
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Q1. Is Zero an Odd Number? If Yes, Explain the Reason.
Ans. No, zero is not an odd number because when odd numbers are divided by 2 then 1 is left behind, as the remainder, but if we divide 0 by 2 then the result is 0.
For example 0/2 = 0
Hence, 0 is not an odd number, it is an even number.
Q2. How will you Determine Whether the Given Number is Odd or Even?
Ans. We will go again by the definition, the numbers which on dividing by 2 leave the remainder of 1 then the given number is an odd number. On the other hand, if we get 0 as the remainder on dividing a given number by 2, then the given number is an even number.
Q3. What are the Types of Odd Numbers? Give a Brief Explanation of Each.
Ans. There are two types of odd numbers, namely, composite odd numbers and consecutive odd numbers.
Composite Odd Numbers: All the positive integers can be classified into composite numbers and prime numbers. The composite numbers have at least one factor other than 1. The composite odd numbers are those composite numbers that are not divisible by 2.
Examples of composite odd numbers from 1 to 50 is:
9, 15, 21, 27, 33, 39, 45, 49.
Consecutive Odd Numbers: These numbers follow an order among them. They have a difference of 2 between them, that is, every two consecutive odd numbers have a difference of 2.
The consecutive odd numbers from 1 to 20 are:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19.