Give Me Example of Odd Numbers

Odd Numbers

Odd Numbers: Numbers are a basic essential part of a human's daily life. Numbers are used in variant form for performing activities such as counting the number of days in a year, number of states in the country, number of members in the family, number of children playing, etc. Odd numbers are one form of numbers that cannot be divided by 2. Odd numbers cannot be divided into two different integers. Examples of odd numbers include 1, 3, 5,7, etc.

Odd numbers are a non-multiple of 2. There is no end to numbers. It can be infinite. Read this article to find all details regarding the definition, examples, type of numbers, etc.

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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 in mathematics.

What are the Types of Numbers?

The number topic is very vast. There are various kinds of numbers like Natural Numbers \(\left(N \right)\), Whole Number \(\left(W \right)\), Integer \(\left(Z \right)\), Rational Number \(\left(Q \right)\), Real Number \(\left( R \right)\), etc. Here, we will discuss only the first three categories, as it involves the odd numbers, which is the main concept to be discussed in this article. Natural numbers, whole numbers and integers contain both even numbers and odd numbers.

What are Even and Odd Numbers?

Any number (natural number, whole number, integer) cannot 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 the below flow chart,

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

What is Odd Number?

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

Facts about Odd numbers:
1- Odd number is an integer i.e. non-multiple of 2.
2- Odd numbers if divided by 2, then there will be a remainder.

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 \(500\) are:

What are the Formulae for Odd and Even Number?

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

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 the 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.

Hundreds	Tens	Units
\(2\)	\(3\)	\(3\)

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

Odd Number	Even Number
\(1892\)\(3\) (ends with an odd number)	\(1892\)\(8\) (ends with an even number)

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.

But, after dividing any number with another number (even or odd), the result may leave with 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:

Operation	result
Odd \( + \) Odd	Even
Odd \( – \) Odd	Even
Odd \( \times \) Odd	Odd
Odd \( \div \) Odd (Only when the denominator is a factor of numerator)	Odd

What are the Types of Odd Numbers?

The numbers which are not the multiple of \(2\) are the 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 \(99\).

What are Some 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 the multiple of \(2\).

Solved Examples – Odd Numbers

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 number ends with \(0,\,2,\,4,\,6\) and \(8\). Some examples of even numbers are \(24,\,820,\,12,\,548\) etc.

Frequently Asked Questions (FAQ) – 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: What are odd numbers called?
Answer: The numbers which are not divisible by \(2\) is called an odd number. 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. In this article, we have only covered the concept of odd numbers and some concepts of even numbers that are related to odd numbers. The details covered are the definition of an odd number list, identification of odd numbers and even numbers, formula to find out odd numbers and even numbers and their properties.

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Give Me Example of Odd Numbers

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