# Even Numbers

**Even Numbers** are integers that are exactly divisible by 2. Whereas an odd number cannot be exactly divided by 2. The examples of even numbers are 2, 6, 10, 20, 50, etc. The concept of even number has been covered in this lesson in a detailed way. Along with the definition of the even number, the other important concepts like first 50 even numbers chart, even numbers up to 100, properties of addition, division, and subtraction are also covered along with solved examples and practice questions.

## What is an Even Number?

Any number that can be exactly divided by 2 is called as an **even number**. Even numbers always end up with the last digit as 0, 2, 4, 6 or 8. Some examples of even numbers are 2, 4, 6, 8, 10, 12, 14, 16. These are even numbers as these numbers can easily be divided by 2. It should be noted that the smallest positive even number is 2. If you pick a number that cannot be divided by 2 is known as an **odd number**. For Example- 1, 3, 5, 7, 9, etc.

### How to Know If a Number is Even or Odd?

To find out whether the given number is odd or even, you need to check the number in one’s (or unit’s) place. That particular number in one’s place will tell you whether the number is odd or even.

- Even numbers end with 0, 2, 4, 6, 8
- Odd Numbers end with 1, 3, 5, 7, 9

Think about the number 3, 842, 917 which ends with an odd number i.e 7. Therefore, the given numbers 3, 842, 917 is an odd number. Thus the number is not an even number Same way, 8, 322 is an even number as it ends with 2.

## List of Even Numbers up to 100

The list of even numbers up to 100 are as follows:

## Properties of Even Numbers

Three important properties of even numbers are given below:

Property | Property Name | Operation | Operation Description | Example |
---|---|---|---|---|

Property 1 |
Property of Addition |
Even + Even = Even | Adding Even and Even, the resulting number is always Even | 14 + 6 = 20 |

Property 2 |
Property of Subtraction |
Even – Even = Even | Subtracting Even from Even, the resulting number is always Even | 16 – 6 = 10 |

Property 3 |
Property of Multiplication |
Even × Even = Even | Multiplying even and even will always result in an even number. | 6 × 4 = 24 |

### Property of Addition

- Adding Even and Odd (or vice-versa), the resulting number is always Odd.

Ex: 8 + 5 = 13,

5 + 18 = 23

- Adding Even and Even, the resulting number is always Even.

Ex: 12+8 = 20

- Adding Odd and Odd, the resulting number is always Even.

Ex: 13 + 9 = 22

### Property of Subtraction

- Subtracting Even from odd (or vice-versa), the resulting number is always Odd.

Ex: 7 – 4 = 3,

10 – 5 = 5

- Subtracting Even from Even, the resulting number is always Even.

Ex: 16 – 6 = 10

- Subtracting Odd from Odd, the resulting number is always Even.

Ex: 21 – 13 = 8

### Property of Multiplication

- Multiplying even and even will always result in an even number.

Ex: 6 × 4 = 24,

12 × 4 = 48

- Multiplying even and odd numbers will result in an even number.

Ex: 4 × 5 = 20,

6 × 3 = 18

- Multiplying odd and odd numbers will always give an odd number.

Ex: 3 × 5 = 15,

5 × 9 = 45

### Even Numbers Solved Problems

**Example 1**:

Are all whole numbers even?

**Solution:**

No, the list of whole numbers which are exactly divisible by two even numbers.

**Example 2:**

Write any four consecutive even numbers between 11 to 19.

**Solution: **

Let A = {11, 12, 13, 14, 15, 16, 17, 18, 19}

Therefore, 12, 14, 16, 18 are 4 consecutive even numbers.

**Example 3:**

Choose the correct answer. The sum of two even numbers

a) is always an even number

b) is always an odd number

c) is sometimes odd and sometimes even

d) may be neither odd nor even

**Solution:**

The correct answer is option a). Even number + Even number = Even number