Even or Odd Numbers

What is the difference between even and odd numbers? If you are also looking for the answer to this question, join us in this article.

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.

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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.

Even NumbersOdd Numbers
Even Numbers are dividable by \(2\).Odd numbers aren’t dividable by \(2\)
If the final digit of a provided number is even, the number is said to be even.If the final digit of a provided number is odd, the number is said to be odd.
Even numbers can be categorized into pairs.You can’t group odd numbers into pairs.

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. \(\color{blue}{99}\)
This image has an empty alt attribute; its file name is answers.png
  1. \(\color{blue}{even}\)
  2. \(\color{blue}{odd}\)
  3. \(\color{blue}{even}\)
  4. \(\color{blue}{odd}\)

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