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Last updated on July 4th, 2025

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Odd Numbers

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Odd numbers are the numbers that are not multiples of 2. They are often observed one after the other in the set of integers. For example: 1, 3, 5, 7, and so on. Odd numbers are useful in creating patterns, sequences, and arithmetic progressions. In this article, we will learn the concept of odd numbers and its significance and applications.

Odd Numbers for Australian Students
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What are odd numbers?

In math, some numbers cannot be divided completely by 2. Such numbers are called odd numbers. They are often represented in the form 2k + 1, where k is any integer.
Odd numbers are not divisible by 2, so it always leaves a remainder.
 

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Difference between Even and Odd Numbers

The main difference between even and odd numbers is the divisibility rule of 2. Here are a few key differences between them:
 

 

Odd Numbers

Even Numbers

Odd numbers cannot be divided evenly by 2.

Even numbers can be evenly divided by 2.

They are expressed in the form 2k +1, where k is an integer.

They are expressed in the form 2k, where k is an integer.

Usually end in 1, 3, 5, 7, and 9.

Their last digit can be 0, 2, 4, 6, or 8.

Adding an even number to an odd number always results in an even number

The sum of even numbers always results in an even number 

Most prime numbers are odd (except 2).

Most even numbers are non-prime (except 2).

 

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How to Identify Odd Numbers?

To easily identify an odd number, check if the given number is not a multiple of 2. An odd number often ends in numbers such as 1, 3, 5, 7, or 9. Moreover, since odd numbers cannot be divided evenly by 2, they always leave a remainder of 1.
 

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List of Odd Numbers from 1 to 100

The list of odd numbers from 1 to 100 lays the foundation for learning more complex odd numbers. Listing these numbers helps identify numbers not divisible by 2. 
We can easily find the odd numbers by simply adding 2 to the previous odd number. For example: adding 2 to the first odd number gives 3, i.e., 1, 1 + 2 = 3, 3 + 2 = 5, 5 + 2 = 7, and so on. Similarly, we can list all the odd numbers from 1 to 100. The last odd number in the list of 1 to 100 is 99, as adding 2 gives 101, which is greater than 100.

 

 


On a number line, odd numbers can be represented by skipping 2 after each number. Positive odd numbers move to the right of 0 (e.g., 1, 3, 5, 7…), whereas negative odd numbers move to the left of 0 (e.g., –1, –3, –5, –7…). 

 

 

The sum of Odd Numbers from 1 to 100


To find the sum of odd numbers from 1 to 100, we will use the formula given below:
S = n/2 (first odd number + last odd number)
Here,
S = Sum of the odd numbers
n = total number of odd numbers between 1 and 100. 
Given that there are 50 odd numbers in the range of 1 to 100,  n = 50.
We now substitute these values into the formula:
S = (50 /2) (1 + 99) 
S = 25 (100)
S = 2500
Thus, all odd numbers between 1 and 100 add up to 2500.
 

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What are the Types of Odd Numbers?

Odd numbers are classified into three types. Let’s now learn how each of them differs:

 

 

Consecutive Odd Numbers


When the numbers in a sequence appear one after the other without any gaps, they are referred to as consecutive numbers. If these numbers are also odd, we call them consecutive odd numbers. For example: 1, 3, 5, 7, and 9. Each consecutive odd number is simply found by adding 2 to the previous number. Note that the difference between any two consecutive odd or even numbers will always result in 2.

 

 

Composite Odd Numbers


A number is said to be composite if it has more than two factors. Composite numbers are of two different types: composite odd numbers and composite even numbers. An odd number that has more than two factors is called a composite odd number. For example, 15 can be considered a composite odd number because it has factors 1,3, 5, and itself.

 

 

Prime Odd Numbers


Numbers that are both odd and prime are called prime odd numbers. These numbers have only two factors: 1 and themselves, and they are not divisible by 2. For example: 3, 5, 7, 11, etc. Keep in mind that all prime numbers are odd except for 2, which is considered the only even prime number.
 

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What are the Properties of Odd Numbers?

We can express all the odd numbers in the form: 2k +1, where k is an integer. For example, 13 can be expressed as 2 × 6 + 1, and  –11 as 2 × (-6)+ 1. We will now look at the different properties of odd numbers.
 

 

Property

Operation

Example

Property of Addition

Odd + Odd = Even

5 + 9 = 14

Property of Subtraction

Odd – Odd = Even 9 – 5 = 4

Property of Multiplication

Odd × Odd = Odd

9 ×  5 = 45

 

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Real-Life Applications of Odd Numbers

We’ve now learned the paramount importance of odd numbers in math. We will now learn why they are significant in real-world situations beyond math:

 

 

  • Odd numbers often create symmetry, which is utilized in seating arrangements, such as in theaters or stadiums.

 

  • Architects use these numbers to design visually pleasing structures or compositions.

 

  • Discounts or offers are often presented in odd amounts. For example: $49 instead of $50.

 

  • Odd numbers are used in traffic control on certain days by using odd-numbered license plates.

 

  • Staircases are often designed with an odd number of steps to help maintain balance
     
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Common Mistakes and How to Avoid Them in Odd Numbers

In math, odd numbers can easily be distinguished. Mostly, students make incorrect applications of odd numbers. Here are a few common mistakes and tips to avoid them:
 

Mistake 1

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Confusion between Odd Numbers and Even Numbers
 

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Students can easily identify odd numbers with its last digit. Sometimes, with its larger odd numbers, students make miscalculations. For example, misidentifying 41, 53, and 65 as even numbers leads to confusion. 
 To easily identify odd numbers, check if they end in 1, 3, 5, 7, or 9.
 

Mistake 2

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Incorrect Addition of Odd Numbers
 

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Students often assume that the sum of two odd numbers always results in an odd number.
Sum of two odd numbers always results in an even number. For example, 3 (odd) + 7 (odd) = 10 (even).
 

Mistake 3

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Incorrectly Applying the Rule for Multiplication
 

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Students incorrectly apply the multiplication rule and assume that the product of two odd numbers is also even. 
Always recall that the product of two odd numbers always results in an odd number. For example: 5 × 3 = 15
 

Mistake 4

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Writing Consecutive Odd Numbers Incorrectly
 

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Forgetting to skip a number when writing consecutive odd numbers leads to inaccurate results.
Ensure that you write the numbers alternately, which has a difference of 2. For example: 1, 3, 5, 7, and 9.
 

Mistake 5

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Misidentifying Prime Odd Numbers
 

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Students consider that most odd numbers are prime numbers. To avoid such mistakes, one should understand the difference between prime numbers and odd numbers. Odd numbers are integers not divisible by 2, while prime numbers are integers which are divisible by 1 and the number itself. For example, 3, 5, 7 are prime numbers while 9, 15 are odd numbers and these are divisible by 3

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Solved Examples of Odd Numbers

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Problem 1

Determine the sum of the first five odd numbers.

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1 + 3 + 5 + 7 + 9 = 25
 

Explanation

The first five odd numbers are: 1, 3, 5, 7, and 9.
We now add the numbers to find the sum:
1 + 3 + 5 + 7 + 9 = 25
 

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Max, the Girl Character from BrightChamps

Problem 2

Amy places 5 books on a shelf. The first book has 15 pages, the second book has 33 pages, and the third book has 45 pages. Is the total number of pages odd or even?

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The total number of pages is 93, which is an odd number.
 

Explanation

 Total number of pages = 15 + 33 + 45 = 93
Since 93 cannot be divided by 2, it is an odd number.

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Max, the Girl Character from BrightChamps

Problem 3

Find the next consecutive odd number after 95.

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 The next consecutive odd number is 97. 
 

Explanation

Since the consecutive numbers have a common difference of 2, we add 2 to the given number:
95 + 2 = 97
 

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Max, the Girl Character from BrightChamps

Problem 4

Check whether the product of two odd numbers, 17 and 5, is an odd number

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the product of 17 and 5 is an odd number.
 

Explanation

 We find the product of 17 and 5 by multiplying them:
17 × 5 = 85 
So, the product of 17 and 5 is an odd number.
 

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Max, the Girl Character from BrightChamps

Problem 5

Abel has 21 cookies and wants to divide them equally among his 6 friends. Will there be any leftover cookies?

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Yes, there will be 3 cookies left.
 

Explanation

We have the total number of cookies = 21
Total number of friends = 6
To find the remainder, we divide 21 ÷ 6 = 3.5
So, there will be 3.5 leftover cookies.
 

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FAQs on Odd Numbers

1.Is 3 the smallest odd number?

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2.Are all prime numbers odd?

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3.What is the result when two odd numbers are multiplied?

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4.How can we find consecutive odd numbers?

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5.How can children in Australia use numbers in everyday life to understand Odd Numbers?

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6.What are some fun ways kids in Australia can practice Odd Numbers with numbers?

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7.What role do numbers and Odd Numbers play in helping children in Australia develop problem-solving skills?

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8.How can families in Australia create number-rich environments to improve Odd Numbers skills?

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Fun Fact

: She loves to read number jokes and games.

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