Odd numbers are numbers that cannot be arranged in pairs. The Ancient Greeks would consider numbers that could not be arranged in two rows as odd. This concept has changed over the millennia. For example, take any multiple of the number 2. You would realize that none of these numbers can be arranged in pairs of 2. Interestingly, all the integers except the multiples of 2 are odd numbers. You will learn about this property later in the article.
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|1.||What are Odd Numbers?|
|2.||List of Odd Numbers|
|3.||Properties of Odd Numbers|
|4.||Types of Odd Numbers|
|5.||FAQs on Odd Numbers|
What are Odd Numbers?
Odd numbers definition is given as those numbers which cannot be divided into two parts equally.
Odd numbers are basically integer numbers that cannot be categorized into groups of two each. For example: 1, 3, 5, 7, etc. Let's visualize it using an example of footwear and cherries. Let us assume that we have footwear in counts of 1, 3, 5, and 7. On the other hand, we have cherries in the counts of 2, 4, 6, and 8. Look at the image given below in order to understand how the pairing of these numbers will work.
It is to note here that the footwear, when odd in number, does not form a pair entirely. One among all remains unpaired. On the contrary, even numbers are those numbers that can be divided into two parts equally. For example: 2, 4, 6, 8, etc.
List of Odd Numbers
Let us have a look at the list of all the odd numbers from 1 to 200 and try to apply the knowledge we have learned here so far. Do note that none of the numbers given here are multiples of 2. You will also note that out of the first 200 numbers, only 100 numbers are odd numbers. Have a look at the list of the odd numbers from 1 to 200 given here.
The definition that we have learned above is applied in this table and it eases our work, doesn't it? Look carefully at the given table and try to notice some similarities between all these numbers given above.Did you notice a pattern in the above odd numbers list?In the odd numbers list, the one's place always remains 1, 3, 5, 7, or 9.
Properties of Odd Numbers
If you try to carry out a few BODMAS operations on the odd numbers, can you come to a common conclusion of all of the numbers? Well yes, there does exist a set of properties that applies not only for the odd numbers given in the list of 1 to 200 but are applicable to any odd number that you may come across. Given below is a list of the properties that will always apply for an odd number. Each of these properties can be explained in a detailed way as given below,
Let's summarize our learning of properties using the table and simulation given below:
|Odd number + Odd number||Even number|
|Odd number - Odd number||Even number|
|Odd number × Odd number||Odd number|
|Odd number ÷ Odd number||Odd number|
Types of Odd Numbers
Odd numbers are a list of all the numbers that are not the multiples of 2. So this seems like a vast set of numbers. So we can have many types of odd numbers starting from whether the odd numbers have factors or not, what is the difference between the two odd numbers, what is the position on the number line of the given odd numbers, and etc. Below given are the two main types of odd numbers.
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 elements. 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
Given below is a list of a few tips and tricks on the topic of odd numbers. These will help you in remembering the concepts faster.An easy method to differentiate whether a number is odd or even: divide it by 2If the number is not divisible by 2 entirely, it'll leave a remainder 1, which indicates a number is an odd number and it can't be divided into 2 parts evenly.If the number is divisible by 2 entirely, it'll leave a remainder 0, which indicates a number is an even number and it can be divided into 2 parts evenly.Odd numbers always have 1, 3, 5, 7, or 9 in their unit's place. Even numbers always have 0, 2, 4, 6, or 8 in their unit's place.
Important Notes on Odd Numbers
Given below is a list of a few important notes on the topic of odd numbers. These will help you in understanding the concepts better.☛Related Articles
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Example 2: Find the sum of the smallest 2 digit number and the largest 2 digit number and also prove that it is an odd number.
To solve the given problem we will follow the steps mentioned below.Step 1: Write down the smallest 2 digit number. The smallest 2 digit number is 10.Step 2: Now, we write down the largest 2 digit number. The largest 2 digit number is 99.Step 3: Now, we have to add the smallest 2 digit number and the largest 2 digit number. Hence, the sum of both the numbers gives 10 + 99 = 109.Step 4: Now, check the unit's place of the number. The unit place of the number is 9, which shows that number is an odd number.
See more: What Is 7 Divided By 9 As A Fraction? What Is 7 Divided By 9
Step 5: Now we will check the divisibility of the number by 2. On dividing the given number 109 by 2, we get the remainder obtained is 1.Hence proved that the sum of the smallest 2 digit number and the largest 2 digit number is an odd number.