Numbers that cannot be organized in pairs are known as odd numbers. Numbers that could not be placed in two rows were considered unusual by the ancient Greeks. Over the millennia, this concept has evolved. Take any multiple of 2 as an example. You’ll see that all of these numbers can be organized in twos. All integers, except for multiples of 2, are odd numbers. This characteristic will be discussed later in this blog.
What are odd numbers?
Odd numbers ar the complete numbers that aren’t dissociative by two. If we tend to divide associate odd range by two, then it’ll leave a remainder as one. Odd numbers finish with the digits one, 3, 5, 7 or 9. Odd numbers ar the other of even numbers. The odd numbers can not be organized in pairs. Odd numbers aren’t the multiples of two.
The samples of odd numbers ar one, 3, 5, 7,31, 43 etc.
For example, thirteen isn’t precisely dissociative by two as a result of it leaves one as remainder after we divide it by two and it ends with three. So, thirteen is associate odd range.
List of Odd Numbers
Observes the list of the odd numbers from 1 to 200 given below.
| 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 |
| 21 | 23 | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 |
| 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | 57 | 59 |
| 61 | 63 | 65 | 67 | 69 | 71 | 73 | 75 | 77 | 79 |
| 81 | 83 | 85 | 87 | 89 | 91 | 93 | 95 | 97 | 99 |
| 101 | 103 | 105 | 107 | 109 | 111 | 113 | 115 | 117 | 119 |
| 121 | 123 | 125 | 127 | 129 | 131 | 133 | 135 | 137 | 139 |
| 141 | 143 | 145 | 147 | 149 | 151 | 153 | 155 | 157 | 159 |
| 161 | 163 | 165 | 167 | 169 | 171 | 173 | 175 | 177 | 179 |
| 181 | 183 | 185 | 187 | 189 | 191 | 193 | 195 | 197 | 199 |
- Did you notice a pattern in the above odd numbers list?
- In the above list, the digit at one place always remains the same like 1, 3, 5, 7, or 9.
Properties of Odd Numbers:
Can you come up with a common conclusion for all of the numbers if you do a few mathematical operations on the odd numbers? Yes, there is a set of attributes that apply not only to the odd numbers in the list of 1 to 200 but to every odd number you may encounter. Some characteristics of odd numbers are given below, make a note of it:
- Addition: The addition of any of the two odd numbers will always give an even number as the answer, eg., the sum of any two odd numbers will always be an even number. For example, 1 (odd) + 3(odd) = 4 (even).
- Subtraction: Subtraction of two odd numbers will always give an even number. For example, 7 (odd) – 1 (odd) = 6 (even).
- Multiplication: Multiplication of any two odd numbers will always give an odd number as an answer. For example, 3(odd) × 5 (odd) = 15 (odd).
- Division: Division of two odd numbers will always give an odd number. For example, 33 (odd) ÷ 11 (odd) = 3 (odd).
Let’s summarize our learning of properties of odd numbers using the table given below:
| Arithmetic Operation | Result |
| Odd number + Odd number | Even number |
| Odd number – Odd number | Even number |
| Odd number × Odd number | Odd number |
| Odd number ÷ Odd number | Odd number |
Odd Numbers and Their Types
A list of all the numbers that are not multiples of 2 is known as odd numbers. This appears to be a large number set. So we can have many different types of odd numbers, such as whether they have factors or not, what the difference between two odd numbers is, where they are on the number line, and so on. The two basic sorts of odd numbers are listed below.
Consecutive Odd Numbers
Let’s say n is an odd number, then the numbers n and n + 2 are grouped under the category of consecutive odd numbers. They always have a difference of 2 between them and are consecutive in nature, hence the name consecutive odd numbers. For example 3 and 5, 11 and 13, 25 and 27, 37 and 39, 49 and 51, and so on. The list is never-ending.
Composite Odd Numbers
As the name suggests, composite means made up of several parts or factors. These types of odd numbers are formed by the product of two smaller positive odd integers. The composite odd numbers from 1 to 100 are 9, 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, 95, and 99.
Tips and Tricks on Odd Numbers
- An easy method to differentiate whether a number is odd or even: divide it by 2.
- If the number is not divisible by 2 entirely, it’ll leave a remainder of 1, which indicates that the number is odd and can’t be divided into 2 parts evenly.
- If the number is divisible by 2 entirely, it’ll leave a remainder of 0, which indicates that it is an even number and can be divided into 2 parts evenly.
- Odd numbers always have 1, 3, 5, 7, or 9 in their unit place. Even numbers always have 0, 2, 4, 6, or 8 in their unit place.
