Even and Odd Numbers

Even and odd numbers are unique sets of whole numbers that are classified as odd and even on the basis of certain properties. It should be noted that there is no number that can be both even and odd. Even numbers are those numbers that are completely divisible by 2, whereas, odd numbers are not completely divisible by 2.

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.

Definition of Even and Odd Numbers

Even and odd numbers can be defined as follows:

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

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.

Let us see the difference between odd and even numbers.

Odd vs Even

The following table shows the difference between even and odd numbers.

Here is 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

An even and odd numbers chart is given below that shows numbers till 100. The numbers shaded in blue are even numbers whereas the numbers shaded in yellow are odd numbers.

Odd and Even Numbers 1 to 100

The following chart shows odd and even numbers from 1 to 100.

• The numbers that end with 0, 2, 4, 6, and 8 are even numbers.
• The numbers that end with 1, 3, 5, 7, and 9 are odd numbers.

How to Find Even and Odd Numbers?

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

• By checking the digit on 'ones' place of the given number, we can identify odd and even numbers easily. Even numbers end with 0, 2, 4, 6, 8, and odd numbers end with 1, 3, 5, 7, and 9.
• By equal grouping: Even numbers can be grouped into pairs whereas odd numbers cannot be grouped in pairs.

Tips on Even and Odd Numbers

• In counting numbers, each alternate number starting from 1 is an odd number, for example, 1, 3, 5, 7, 9, 11, 13, and so on are odd numbers.
• Similarly, every alternate number starting from 2 is an even number, for example, 2, 4, 6, 8, 10, 12, and so on are even numbers.
• 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

• Even or Odd Calculator
• Rational Numbers
• Irrational Numbers
• Cardinal Numbers
• Ordinal Numbers

What is the Definition of Even and Odd Numbers?

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. In other words, an even number is defined as a number that can be divided into two equal groups. For example, the numbers 22, 34, 70, 68, and so on are even numbers. On the other hand, an odd number is defined as a number that cannot be divided into two equal groups. For example, numbers such as 13, 25, 37, 49, and so on, are odd numbers.

Is Infinity Odd or Even?

Infinity is not an actual representation of a number. It is 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, we need to observe the last digit of the number, that is, the digit in ones place. When that digit is any of the following numbers, 0, 2, 4, 6, or 8, then the number is even, whereas, when the last digit is 1, 3, 5, 7, or 9, then the number is odd.

What is the Smallest 6-digit Even Number?

The smallest 6-digit even number is 100000, because after 100000, the next even number is 100002, and the even number before 100000 is 99998 which is a 5-digit number.

Are Decimal 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.

What are Prime Even and Odd Numbers?

A prime number is a number that has only two factors, 1 and the number itself. For example, 3, 5, 9, 11, 13, 15, 47, and so on. Even numbers are those numbers that are completely divisible by 2. For example, 2, 4, 26, 78, and so on. Odd numbers are those numbers that are not completely divisible by 2. For example, 1, 3, 9, 21, and so on.

• Therefore, if we need to identify prime even numbers, we have 2 as the only even number that is prime, the rest of the even numbers are not prime.
• Prime odd numbers are those odd numbers that are prime. This means odd numbers that have only 2 factors (1 and the number itself) are called prime odd numbers. For example, 3, 5, 7, 11, 13, and so on are prime odd numbers. It should be noted that odd numbers like 9, 15, 21, and so on are not prime.

What is the Sum of an Even and Odd Number?

The sum of an even and an odd number is an odd number. For example, 6 + 11 = 17. Here 6 is an even number, 11 is an odd number, and their sum 17 is an odd number.

What is the Product of an Even and Odd Number?

The product of an even and an odd number is an even number. For example, 22 × 7 = 154. Here 22 is an even number, 7 is an odd number, and their product 154 is an even number.

Is 14 Even or Odd?

14 is an even number because it is divisible by 2. It can be divided into 2 equal groups of 7.

What is the Difference Between Odd and Even Numbers?

The difference between odd and even numbers is as follows.

• Even numbers are completely divisible by 2 but odd numbers are not completely divisible by 2.
• Even numbers can be grouped into pairs but odd numbers cannot be grouped into pairs.
• The last digit of an even number is always 0, 2, 4, 6, and 8, whereas the last digit of an odd number is always 1, 3, 5, 7, and 9.