Even Numbers

Numbers that are exactly divisible by 2, without any remainder, are called even numbers. Even numbers are also multiples of 2. If a number’s last digit is 0, 2, 4, 6, or 8, then it is an even number. 0, 2, 4, 6, 8, 10, and 12 are the first few even numbers.

For example, let us divide an even number by 2.
10 ÷ 2 = 5

Here the quotient is 5, and there is no remainder. Hence, 10 is an even number.
 

We can find even numbers using various methods. 

• If we check whether a number is exactly divisible by 2, without any remainder, then the number is even.
  For instance, 76 ÷ 2 = 38 (it is an even number) 
  35 ÷ 2 = 17.5 (it is not an even number). 
   
• If the last digit of a number ends in 0, 2, 4, 6, or 8, the number will be even. For example, 7632, 1000, 654, and 498 are even numbers. 

Consecutive even numbers follow one another from the smallest to the largest values, and they increase by 2. The common difference between two consecutive even numbers is always 2. Here is a list of a few consecutive even numbers from 0 to 20. 
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 are consecutive even numbers. 

Natural numbers are a set of numbers that start from 1 till infinity such as 1, 2, 3, 4, and so on. Even natural numbers are the numbers that begin from 2 and are divisible by 2, without any remainder. The first few even natural numbers are 2, 4, 6, 8, and 10. The main difference between even numbers and even natural numbers is that even numbers start with zero, whereas even natural numbers start with 2. 
 

We use a number line to represent numbers in order. We can easily mark even numbers on this imaginary line by keeping the same difference between two even numbers, which means each number increases by 2.

For example, if we mark 0 as an even number and move 2 values forward, we reach the positive integer 2. Again, from 2, we jump and reach 4. This same pattern follows on the left side of the number line. Here is an image of even numbers on a number line. 

The properties of even numbers are listed below: 

 Property of addition of even numbers: 

• If we add two even numbers the sum is always an even number. For example, 66 + 10 = 76.
   
• If we add an even number and an odd number, the result will be an odd number. For instance, 55 + 12 = 67. 
   
• If we add two odd numbers the sum is an even number. For example, 33 + 59 = 92. 

Property of subtraction of even numbers:

• Subtracting two even numbers results in an even difference. For instance, 32 - 6 = 26.
   
• When we subtract an even number from an odd number, the difference is odd. For example, 50 - 9 = 41.
   
•  If we subtract two odd numbers, the difference will be an even number. For instance, 69 - 33 = 36. 

Property of Multiplication of Even Numbers:

• The product of multiplying two even numbers is always an even number. For example, 12 × 54 = 648.
   
• Multiplying an even number by an odd number also gives an even product. 
   
• For instance, 10 × 3 = 30.

Property of Division of Even Numbers:

Even numbers can be exactly divided by 2 without a remainder. For example, 62 ÷ 2 = 31 (with the remainder 0).

Even numbers are helpful in our daily life calculations and mathematics, as they help organize and group items equally. Here are some real-world applications of even numbers: 
 

• We can use even numbers to divide items, money, or time equally and fairly distribute them among us. For example, if we have $1000 among 10 people, we can equally distribute it so that each one gets $100. 
   
• Managers can schedule the work shifts for their employees accordingly using even numbers. For example, if there are 6 employees in a company, the manager can schedule the day among them, and each employee should work for 4 hours a day. 
   
• Sports coaches and players can form groups with even numbers of players to ensure the number of players is balanced and plan their matches wisely. For instance, in a basketball match, there are a total of 10 players on the court. 
   
• Engineers can use even numbers to divide and design structures in their work. Ensuring proper balance and stability. For example, engineers can divide a 586 sq ft house into two equal parts for easier management.