Even and Odd Numbers
In math, whole numbers can be further classified into even and odd numbers. Both odd and even numbers 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 those numbers that are completely divisible by 2, whereas, odd numbers are not completely divisible by 2.
| 1. | What are Even and Odd Numbers? |
| 2. | Difference Between Even and Odd Numbers |
| 3. | Properties of Even and Odd Numbers |
| 4. | Even and Odd Numbers Chart |
| 5. | FAQs on Even and Odd Numbers |
What are Even and Odd Numbers?
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 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.
Difference between Even and Odd Numbers
The following table shows the difference between even and odd numbers.
| Even Numbers | Odd Numbers |
|---|---|
| Even Numbers are completely divisible by 2. | Odd numbers are not completely divisible by 2 |
| If the last digit of a given number is even, then that number is considered to be even. | If the last digit of a given number is odd, then that number is considered to be odd. |
| Even numbers can be grouped into pairs. | Odd numbers cannot be grouped into pairs. |
Properties of 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
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.
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 1,3,5,7,9.
- 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 the counting numbers, each alternate number starting from 1 is an odd number and each alternate number starting from 2 is an even number.
- 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
FAQs on Even and Odd Numbers
What are 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. For example, numbers such as 13, 25, 37, 49, and so on, are odd numbers, and the numbers 22, 34, 70, 68, and so on are even 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 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 Even Number?
The smallest even number is 2. So, the smallest six-digit even number is 222222.
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, 13, 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 the prime numbers that are even, we have 2 as the only even number that is prime, the rest of the even numbers 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, where 6 is an even number, 11 is an odd number, and the sum is an odd number.
What is the Product of an Even and Odd Number?
The sum of an even and an odd number is an even number. For example, 22 × 7 = 154.