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# Even Numbers

An even number is a number which is an integer that is evenly divisible by an integer 2, i.e., the remainder will always comes out to be zero whenever it’s divisible by 2; otherwise, the number becomes an odd number.

An even number is formally defined as an integer of the form n = 2x, where x is an integer.
Mathematically it’s defined as a set as Even numbers = {2x; for all x belonging to integers}, whereas an odd number is an integer of the form n = 2x + 1.
Few examples of even numbers are −14, 0, 18, and 174.In simpler words, starting from zero and then all the multiples of two comes under the category of even numbers, as shown below:

A number (i.e., an integer) which is in the decimal system is picked up as an even number only if its last digit is even.
That is, if the last digit is 0, 2, 4, 6, or 8, then it’s even.

In particular, a number which is in binary system is determined as even if and only if the sum of its all digits comes out to be even.
To summarize, we can say that any integer that can be divided exactly by 2 is known as an even number and if it is not an even number, then it is called an odd number.

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## Properties

Properties of Even Numbers:
We know that in simple arithmetic operations, the multiplication and addition are always commutative and associative, and in particular multiplication is distributive over addition.
But in case of subtraction, its in parity is very much similar to addition, so subtraction also has these properties.

Addition and Subtraction of Even Numbers:
Whenever we will add or subtract two even numbers the resulting number would be an even number only. That is, even ± even = even.

Whenever we will add or subtract one even number with an odd number then the resulting number would be an even number only. That is, even ± odd = odd.

Whenever we will add or subtract two odd numbers the resulting number would be an even number only. That is, odd ± odd = even.

Multiplication of Even Numbers:
Whenever we will multiply two even numbers the resulting number would be an even number only. That is, even × even = even.

Whenever we will multiply one even number with an odd number the resulting number would be an even number only.
That is, even × odd = even.

Division of Even Numbers:
Whenever we will divide two integers, the resulting number may or may not be an integer. Consider 1 divided by 3, which is neither even nor odd, and to be categorized as even or odd, it has be an integer and $\frac{1}{3}$ is not an integer.

## Even Numbers Example

Example 1: Which group has only even numbers?
A.  -14, -10, and -6 and B. -4, -8, and 3
Solution: Group A is only of even numbers.

Example 2: Make a chart of integers from 1 to 100, highlighting even number with blue color.
Solution:  The following is a chart of even numbers out of 1 to 100.

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