What are Odd Numbers: Definition and Examples

Students who have just been introduced to the odd and even number system often get confused about which one is odd and which one is even. So first let’s get clear that numbers that are divisible by 2 are called even numbers. On the other hand, the numbers that are not divisible by 2 are odd numbers. Examples of odd numbers include 1, 3, 5, 7, etc.

Below here in this article, we have explained in more detail about both odd and even numbers as well as what other types of numbers exist. So, keep reading to understand what are even and odd numbers.

What is a Number?

Numbers are the building blocks of mathematics. These can be used to count or measure something. It has a very important role in our daily life and mathematics.

What are Even and Odd Numbers?

Any number (natural number, whole number, integer) not be divisible by \(2\) is called an odd number. When we divide an odd number by \(2,\) it leaves the remainder as \(1\) always. Examples of some odd numbers are \(11,\,173,\,107,\,979\), etc. Odd numbers end with the digits \(1,\,3,\,5,\,7\) and \(9.\)

Any number (natural number, whole number, integer) divisible by \(2\) without leaving any remainder is called an even number. Examples of even numbers are \(2,\,72,\,422,\,38\), etc. Even numbers end with the digits \(0,\,2,\,4,\,6\) and \(8.\)

We can better understand the concept of even and odd numbers by taking a look at the below flow chart:

Even odd numbers are available on both sides of the number line. This means that even and odd numbers are both positive and negative. On the right side of the number line, every alternative number from \(0\) are positive even number, and every alternative number from \(1\) is a positive odd number. Similarly, on the left side of the number line, every alternative number from \(0\) are negative even number, and every alternative number from \( – 1\) is a negative odd number.

What is an Odd Number?

An odd number is a number that is not divisible by \(2.\) When we divide an odd number by \(2,\) it always leaves a remainder \(1\). Positive odd numbers start from \(1\), i.e., \(1\) is the first positive odd number. Every alternative number from \(1\) is an odd number. It is not in the multiple of \(2.\)

Chart of Odd Numbers from 1 to 100

All the odd numbers are coloured in green and all the even numbers are coloured in orange.

Odd Number List

List of Odd Numbers between 1 to 10: The odd numbers between \(1\) to \(10\) are \(1, 3, 5, 7\) and \(9.\) There are five odd numbers from \(1\) to \(10.\)

List of Odd Numbers between \(1\) to \(500\): The list of odd numbers from \(1\) to \(500\) is given below:

Formulae for Odd and Even Numbers

Formula for Odd Numbers: \(2n + 1\) where \(n \in Z\) (Whole numbers)

The formula for Even Numbers: \(2n\) where \(n \in Z\) (Whole numbers)

How to Identify Odd Numbers?

The numbers ending with (or units place digit) the digits \(1,\,3,\,5,\,7\) and \(9\) are odd numbers.

Example: \(11,\,233,\,5735,\,9819\) etc.

As the number \(233\) ends with the digit \(3\) (odd number), the given number is an odd number.

Even numbers end with \(0,\,2,\,4,\,6\) and \(8.\) On the other hand, an odd number ends with \(1,\,3,\,5,\,7\) and \(9.\)

What are the Properties of Odd Numbers?

The properties of odd numbers are as follows:

Property of Addition: By adding two odd numbers, we get an even number.
Example: \(3+5=8\)
Property of Subtraction: By subtracting two odd numbers, we get an even number.
Example: \(99-11=88\)
Property of Multiplication: By multiplying two odd numbers, we get an odd number.
Example: \(5×3=15\)

Property of Division of Two Odd Numbers

As seen above, there are a couple of rules to get the result after addition, subtraction, and multiplication of two even numbers, two odd numbers, or an even number and an odd number. In all those cases, it gives the result as an integer.

However, after dividing any number with another number (even or odd), the result may be a fraction. And fraction is neither an even nor an odd number; they are not whole numbers also.

Example 1: We cannot say \(\frac{2}{{10}}\) is an odd number or even number. (though \(2\) and \(10\) both are even numbers).

Example 2: We cannot say \(\frac{3}{{15}}\) is an odd number or even number. (though \(3\) and \(15\) both are odd numbers)

The terms ’even number’ and ‘odd number’ are also used for whole numbers. The division of two odd numbers is an odd number (it is only possible), only when the denominator is a factor of the numerator.

Example: \(\frac{3}{{33}} = 11\)

In short:

Types of Odd Numbers

The numbers which are not the multiple of \(2\) are odd numbers. The list of odd numbers is vast. Still, let us discuss two main types of odd numbers.

1. Consecutive odd numbers: Suppose n is an odd number, then the numbers \(n\) and \(n + 2\) are grouped under the category of consecutive odd numbers.
Example: Suppose \(5\) (the value of \(n\)) is an odd number, then \(n + 2 = 5 + 2 = 7\) (odd number).
So, \(5\) and \(7\) are two consecutive odd numbers.

2. Composite odd numbers: These types of odd numbers are formed by the product of two smaller positive odd integers (excluding \(1\)). The list of composite odd numbers from \(1\) to \(100\) are given below, \(9,\,15,\,21,\,25,\,27,\,33,\,35,\,39,\,45,\,49,\,51,\,55,\,57,\,63,\,65,\,69,\,75,\,77,\,81,\,85,\,87,\,91,\,93,\,95\) and \(99\).

Facts About Odd Numbers and Even Numbers

The addition of one even number and one odd number is always an odd number. Example: \(14 + 53 = 67\)

Subtraction of one even number from another even number is an even number. Example: \(22 – 12 = 10\)

Subtraction of one even number from one odd number is an odd number. Example: \(991 – 2 = 989\)

Addition of two even numbers is an even number. Example: \(15836 + 96378 = 112214\)

Multiplication of one even number and one odd number is an even number.
Example: \(8 \times 3 = 24\)

Multiplication of two even numbers is an even number. Example: \(8 \times 8 = 64\)

Odd numbers are not multiples of \(2\). But even numbers are multiples of \(2\).

Solved Examples

Question-1: Explain \(67002\) is an odd number or even number.
Answer: As the number \(67002\) ends with the digit \(2,\) it is an even number.

Question-2: Explain \(9577\) is an odd number or even number.
Answer: As the number \(9577\) ends with the digit \(7\), it is an odd number.

Question-3: When we divide \(345671\) by \(2\), what will be the remainder?
Answer: As the unit digit of the number \(345671\)  is \(1\) which is an odd number, we will get the remainder as \(1\) only. As we divide an odd number by \(2\), the remainder is always \(1\).

Question-4: Are the following numbers odd?
a. \(89 – 45\)
b. \(24 + 35\)
c. \(66 \div 2\)
Solution:
a. \(89 – 45 = 44,\) divisible by \(2.\) So, the result is not an odd number.
b. \(24 + 35 = 59,\) not divisible by \(2.\) So, it is an odd number.
c. \(66 \div 2 = 33,\) not divisible by \(2.\) So, it is an odd number.

Question-5: How many odd numbers are there between \(1\) to \(100\)?

Answer: There are \(50\) odd numbers (and \(50\) even numbers) between \(1\) to \(100.\)

Question-6: Is \(190\) an even number?
Answer: Yes, \(190\) is an even number, as it is divisible by \(2\) or it ends with the digit \(0.\)

Question-7: How many odd numbers and even numbers between \(1\) to \(1000\)?
Answer: There are \(500\) odd numbers and \(500\) even numbers between \(1\) to \(1000.\)

Question-8: What is the smallest positive odd number?
Answer: \(1\) is the smallest positive odd number.

Question-9: Is number \(0\) an odd or even number?
Answer: \(0\) is an even number, as it is the multiple of \(2.\)

Question-10: What is an even number?
Answer: When we divide a number by \(2\), if we get the remainder as zero, it is called an even number. Even numbers ends with \(0,\,2,\,4,\,6\) and \(8\). Some examples of even numbers are \(24,\,820,\,12,\,548\), etc.

FAQs on Odd Numbers

Here are some of the most frequently asked questions related to Odd Numbers:

Question-1: Is \(27\) an odd number?
Answer: Yes, \(27\) is an odd number. As the last digit of \(27\) is \(7\) (odd number), the number \(27\) is an odd number and when we divide it by \(2,\) we get the remainder \(1.\)

Question-2: What are the odd numbers from \(1\) and \(100\)?
Answer: The list of odd numbers from \(1\) to \(100\) are \(1,\,3,\,5,\,7,\,9,\,11,\,13,\,15,\,17,\,19,\,21,\,23,\,25,\,27,\,29,\,31,\,33,\,35,\,37,\,39,\,41,\,43,\,45,\,47,\,49,\) \(51,\,53,\,55,\,57,\,59,\,61,\,63,\,65,\,67,\,69,\,71,\,73,\,75,\,77,\,79,\,81,\,83,\,85,\,87,\,89,\,91,\,93,\,95,\,97,\,99\).

Question-3: Is \(1\) an odd or even number?
Answer: \(1\) is an odd number. As it is not divisible by \(2.\) Again, we can say, if the number cannot be divided by \(2,\) is an odd number.

Question-4: Which numbers are called odd numbers?
Answer: The numbers which are not divisible by \(2\) are called odd numbers. The odd number ends with the digits \(1, 3. 5, 7\) and \(9.\) Some examples of odd numbers are \(23, 17, 237\), etc.

Question-5: What are the odd numbers between \(1\) to \(30\)?
Answer: The list of odd numbers from \(1\) to \(30\) are \(1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.\)

Question-6: Is \(101\) an odd number?
Answer: Yes, \(101\) is an odd number. As the last digit of \(101\) is \(1\) (odd number), the number \(101\) is an odd number and when we divide it by \(2\), we get the remainder \(1.\)

Conclusion

As the concept of numbers is vast, we have only covered the concept of odd numbers and some concepts of even numbers that are related to odd numbers in this article. The details covered are the definition of an odd number, identification of odd numbers and even numbers, and the formula to find out odd numbers and even numbers and their properties.

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