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 2. You would realize that all 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.
|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 positive integers that cannot be categorized into groups of two. 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 pairs 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, 4 can be divided into 2 pairs of 2, 8 can be divided into 4 pairs of 2, 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 digit at the ones place always remains 1, 3, 5, 7, or 9.
Properties of Odd Numbers
If you try to carry out a few arithmetic 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:
- Addition: The addition of two odd numbers will always give an even number, i.e., the sum of two odd numbers is always an even number. For example, 3 (odd) + 5 (odd) = 8 (even).
- Subtraction: Subtraction of two odd numbers will always give an even number. For example, 7 (odd) - 1 (odd) = 6 (even).
- Multiplication: Multiplication of two odd numbers will always give an odd number. For example, 3 (odd) × 7 (odd) = 21 (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:
|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 two odd numbers, what is their position on the number line, etc. Give below 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 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
Given below is a list of a few tips and tricks on 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 2.
- If the number is not divisible by 2 entirely, it'll leave a remainder 1, which indicates that the number is an odd number and can't be divided into 2 parts evenly.
- If the number is divisible by 2 entirely, it'll leave a remainder 0, which indicates that it 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 units place. Even numbers always have 0, 2, 4, 6, or 8 in their units place.
Given below is the list of topics that are closely connected to odd numbers. These topics will give you a glimpse of how such concepts are covered in Cuemath.
Odd Number Examples
Example 1: Determine whether 135 is an odd number or not.
We can find this out using any of the given two methods:
Method 1: Check the units place digit of the number. The unit place of the number is 5, which shows that number is an odd number.
Alternative Method: We have to check the divisibility of the number by 2. On dividing the given number 135 by 2, we get the remainder as 1. This proves that 135 is an odd number.
Therefore, we determined that the number 135 is odd.
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, 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 numbers gives 10 + 99 = 109.
Step 4: Now, check the units place digit of the number. The unit place of the number is 9, which shows that number is an odd number.
Therefore, the sum of the smallest 2-digit number and the largest 2-digit number is 109 which is odd.
FAQs on Odd Numbers
What are Odd Numbers in Math?
In math, all the numbers that are not the multiples of 2 are odd numbers. For example, 3, 5, 7, 9, etc.
What are the Odd Numbers From 1 to 100?
The list of odd numbers from 1 to 100 is: 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.
What is the Difference Between an Odd Number and an Even Number?
The numbers which can be divided into two parts evenly are called even numbers whereas odd numbers cannot be divided into equal pairs.
What are Two Consecutive Odd Numbers?
Two consecutive odd numbers are those numbers that are odd and have a difference of 2 between them. For example 3 and 5, 11 and 13, etc.
Is 0 an Even or Odd Number?
0 is an even number as it is a multiple of 2.
What is the Mean of First Five Odd Numbers?
To determine the mean of the first five odd numbers we need to follow the steps listed below:
- List the first five odd numbers, they are 1, 3, 5, 7, and 9.
- Calculate the sum → 1 + 3 + 5 + 7 + 9 = 25.
- Applying mean formula = Mean of any n numbers = (Sum of n numbers) / n = 25/5 = 5.
Therefore, the mean of the first five odd numbers is 5.
How Many Odd Numbers are There Between 36 and 53?
The list of odd numbers that lie between 36 and 53 are 37, 39, 41, 43, 45, 47, 49, 51. Hence, there are a total of 8 odd numbers between 36 and 53.
Is Number 1 Odd or Even?
1 is an odd number. This is because it has digit 1 at the units place. Also, if you try to divide 1 by 2, you will get a remainder as 1. Hence, 1 is an odd number.
What is the Formula of Odd Numbers?
The odd number formula to represent an odd number can be given as 2n + 1, where, n ∈ W (whole numbers).
What is the HCF of Two Consecutive Odd Numbers?
What are Even and Odd Numbers?
All whole numbers can be categorized into two parts: even and odd numbers. Even numbers are the ones whose units place digit is either 0, 2, 4, 6, or 8, and odd numbers are ones whose units place digit is either 1, 3, 5, 7, or 9. Examples of even numbers are 2, 4, 6, 8, 10, 12, 14, 16, etc, and the examples of odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, etc.
What is the Smallest Odd Number?
1 is the smallest odd number.