# Even or Odd Numbers

## Odd or Even Numbers

In mathematics, whole numbers may get further categorized into odd and even numbers. Both even and odd numbers are a distinctive set of numbers, while no digit can be odd and even at the same time. It must be either odd or even.

## What are Odd and Even Numbers?

• Even Numbers: Numbers which can be divided by $$2$$, with zero remaining is known as even numbers. Even numbers are divisible into two identical groups.
• Odd Numbers: Numbers you can’t divide by $$2$$ and leave $$1$$ as a remainder ae known as odd numbers. Odd numbers can’t get divided into two identical groups.

## Set Representation of Odd and Even Numbers

• A set of even numbers is symbolized as {$$x: x = 2k where k ∈ W$$}, where $$k$$ is an integer and $$W$$ is a set of whole numbers.
• A set of odd numbers is symbolized as {$$x: x = 2k – 1 where k ∈ N$$}, where $$k$$ is an integer and $$N$$ is a set of natural numbers.

## Way to Locate Odd and Even Numbers?

You can see if a particular number is odd or even via utilizing one of these methods:

• Via checking the figure in the ‘ones’ position of the particular number, you are able to determine eve or odd numbers with ease. Even figures end with $$0,2,4,6,8$$ and the odd figures end with $$1,3,5,7,9$$.
• Via equivalent grouping: Even numbers are able to be grouped into pairs and odd numbers can’t be grouped into pairs.

## Hints regarding Odd and Even Numbers

• When counting digits, each alternate figure beginning with $$1$$ is called an odd number as well as each alternate figure beginning with $$2$$ is called an even number.
• A simple method of finding if a provided digit is odd or even is by checking if you can divide it by $$2$$.
• Non-integer figures are not odd or even, like $$3/4$$, $$0.43$$, or infinity.

The subsequent table displays the distinction between odd and even numbers.

## Odd and Even Number Properties

The following is a list of several characteristics of odd and even numbers:

• Even number plus an Even number $$=$$ An Even Number
• Even number plus an Odd Number $$=$$ An Odd Number
• Odd number plus an Odd Number $$=$$ An Even Number
• Even numbers minus an Even Number $$=$$ An Even Number
• Even Number minus an Odd Number $$=$$ An Odd Number or an Odd Number minus an Even Number $$=$$ An Odd Number
• Odd number minus an Odd Number $$=$$ An Even Number
• Even Number times an Even Number $$=$$ An Even Number
• Even number times an Odd Number $$=$$ An Even Number

### Even or Odd Numbers – Example 1:

Identify whether the number is even or odd.

$$32$$

Solution:

Any number whose last digit is $$0, 2, 4, 6$$, or $$8$$ is an even number. So, $$32$$ is an even number

### Even or Odd Numbers – Example 2:

Find the odd number in this group

$$8,14,22,41,12$$

Solution:

Odd figures end with $$1,3,5,7,9$$. So, in the above group just $$41$$ is an odd number.

## Exercises for Even or Odd Numbers

Identify whether each number is even or odd.

1. $$\color{blue}{84}$$
2. $$\color{blue}{25}$$
3. $$\color{blue}{62}$$
4. $$\color{blue}{99}$$
1. $$\color{blue}{even}$$
2. $$\color{blue}{odd}$$
3. $$\color{blue}{even}$$
4. $$\color{blue}{odd}$$

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