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Even and Odd Numbers

In math, whole numbers can be further classified into even and odd numbers. Both are a unique set of numbers and there is no number that can be both even and odd. A number can be an even or an odd number. Even numbers are the ones that are completely divisible by 2, whereas, odd numbers leave a remainder one while dividing by 2.

1. Even and Odd Numbers Definition
2. Properties of Even and Odd Numbers
3. Even and Odd Numbers Chart
4. How to Check a Number is an Even or an Odd Number?
5. Solved Examples 
6. Practice Questions 
7. FAQs 

Even and Odd Numbers Definition

An even number is defined as a number that can be divided into two equal groups. On the other hand, an odd number is defined as a number that cannot be divided into two equal groups.

Even and odd numbers can also be characterized as:

  • Even Number: A number that is divisible by 2, leaving a remainder 0 is called an even number.
  • Odd Number: A number that is not divisible by 2 and leaves a remainder '1'.

Set Representation of Even and Odd Numbers

  • The set of even numbers is represented as {x : x = 2k where k ∈ W}, where k is an integer and  'W' is the set of whole numbers.
  • The set of odd numbers is represented as {x : x = 2k – 1 where k ∈ N}, where 'k' is an integer and  'N' is the set of natural numbers.

Properties of Even and Odd Numbers

Here's a list of a few properties of even and odd numbers:

  • Even Numbers + Even Number = Even Number. For example, 10 + 8 = 18
  • Even number + Odd Number = Odd Number. For example, 14 + 21 = 35
  • Odd number + Odd Number = Even Number. For example, 23 + 5 = 28.
  • Even numbers - Even Number = Even Number. For example, 76 - 12 = 64
  • Even Number - Odd Number = Odd Number. For example, 28 - 3 = 25 OR Odd Number - Even Number = Odd Number. For example, 29 - 12 = 17
  • Odd number - Odd Number = Even Number. For example, 43 - 11 = 32
  • Even Number × Even Number = Even Number. For example, 8 × 6 = 48
  • Even number × Odd Number = Even Number. For example, 12 × 9 = 108 

Even and Odd Numbers Chart

Given below is an even and odd numbers chart. It shows numbers till 100. The numbers shaded in blue are even numbers whereas the numbers shaded in yellow are odd numbers. We can clearly see that the even numbers end with 0,2,4,6,8 and the odd numbers end with 1,3,5,7,9.

Even and Odd Numbers

How to Check a Number is an Even or an Odd Number?

We can check whether a given number is an even or an odd number using either of the following ways:

  • By checking if the digit at the “ones” place of the number is even or odd, we can identify them easily.:(Pls rephrase - By checking if the "ones" place digit of a number is an even number).Even numbers end with 0,2,4,6,8 and odd numbers end with 1,3,5,7,9.
  • By equal grouping: Even numbers can be grouped into pairs whereas odd numbers can't be grouped in pairs.

Important Notes

  • In the counting numbers, each alternate number is an odd number starting from 1 and an even number starting from 2.
  • An easy way to find out whether a given number is even or odd is to check its divisibility by 2.
  • Non-integer numbers are neither even nor odd, such as 1/2, 0.88, or infinity.

Related Articles

Check out these interesting articles t know more about even and odd numbers and their related topics.

 

Solved Examples

  1. Example 1: Ron had 40 balls in all. He gave 29 out of the total number of balls to his friend. Determine if the balls left with him are even or odd in number.

    Solution:

    Ron gave 29 out of 40 balls, so he had 11 balls left with him because 40 - 29 = 11. Since 11 cannot make equal pairs of 2, it is an odd number. 

  2.  

    Example 2: Determine whether 903 is an odd number or not.

    Solution:

    First, we need to check the digit at the units or the ones place of the number. In the ones place, the number is 3. On dividing the given number 903 by 2, we get the remainder as 1. This proves that 903 is an odd number. 

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FAQs on Even and Odd Numbers

What are Odd and Even Numbers with Examples?

The numbers ending with 1,3,5,7 and 9 are odd numbers whereas the numbers ending with 0,2,4,6 and 8 are even numbers. For example, numbers such as 13, 25, 37, 49, etc are odd numbers, and the numbers 22, 34, 70, 68, etc are even numbers.

Is Infinity Odd or Even?

Infinity isn't an actual representation of a number. It's a concept. Therefore it is neither odd nor even. However, a set may be called an even set, considering all even numbers from 2 to infinity.

What is the Smallest Odd Number?

The smallest odd number is '1'. It is neither a prime number nor a composite number by convention. 

How to Classify Even and Odd Numbers?

To classify an even or odd number, look at the digit to the very right of the number, that is the digit at ones place. When that digit is either 0, 2, 4, 6, or 8, then the number is even whereas when the digit is 1, 3, 5, 7, or 9, then the number is odd.

What are the Odd Numbers from 1 to 100?

The set of odd numbers from 1 to 100 include all alternate numbers starting from 1 till 99.

What is the Smallest 6-digit Odd Number?

The smallest even number is 2. So, the smallest six-digit even number is 222222.

Are Decimals Numbers Considered Even or Odd Numbers?

Since decimals are not whole numbers, they cannot be classified as even or odd numbers. The same is the case with fractions as well.

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