 Parity Properties of Even and Odd Numbers – Definition, Facts, Examples

Numbers play an important role in our day-to-day life. A number is a value that is used to express the quantity, calculations, reading numbers, counting, etc. Real numbers are classified as even numbers and odd numbers. A number that is divisible by 2 and leaves remainder as ‘0’ is known as an even number. A number that is divisible by 2 and leaves remainder as ‘1’ is known as an odd number.

Even numbers are those numbers that can be divided into two equal groups. Whereas odd numbers are the numbers that cannot be divided into two equal groups. In this article, we will discuss in detail the even and odd numbers, properties of even and odd numbers here. So, the students can gain more knowledge on even and odd numbers properties and can solve various kinds of problems easily.

Do Refer:

Properties of Even and Odd Numbers

Let us have a look at the properties of even and odd numbers before you start solving the problems.

Even+Even

• An Even number is divisible by 2 and leaves the remainder ‘0’.
• An odd number is not completely divisible by 2 and leaves the remainder ‘1’.
• An even number ends with 0, 2, 4, 6, and 8.
• An odd number ends with 1, 3, 5, 7, and 9.
• The sum of two even numbers is an even number.
• The sum of two odd numbers is an even number.
• The sum of even and an odd number is an odd number.
• The product of two even numbers is an even number.
• The product of an even and odd number is an even number.

Parity Properties of Even and Odd Numbers Even and Odd Numbers Examples

Let us check the properties of even and odd numbers with some examples.
Example 1.
Add two odd numbers 3 and 5

Solution:
Two odd numbers 3 + 5 = 8
8 is an even number
Adding two odd numbers is an even number.

Example 2.
Add any two even numbers to prove the property “The sum of two even numbers is an even number.”

Solution:
Any two even number 2 + 4 = 6
6 is an even number
Adding two even numbers is an even number.

Example 3.
Addition of one even number and one odd number.

Solution:
One even number is 24
One odd number is 25
24 + 25 = 49
Adding of one even number and one odd number is an odd number.

Example 4.
Addition of any two odd numbers.

Solution:
Any two odd numbers is 35 + 37 = 72
72 is an even number
Adding of the odd numbers is an even number.

Example 5.
What is the sum of 5 and 16?

Solution:
5 + 16 = 21
21 is an odd number
Addition of one even number and one odd number is an odd number.

FAQs on Even and Odd Numbers

1. Why zero is an even number?

Zero is an even number because it is an integer multiple of 2.

2. Write an example to show that sum of two even numbers is an even number?

Let us consider 2 and 6.
2 + 6 = 8
8 is an even number.
Thus we can say that the sum of two even numbers is an even number.

3. Show that the sum of an even number and an odd number is an odd number.

Let us consider 2 and 5
2 + 5 = 7
7 is an odd number.
By this, we can prove that the sum of an even number and an odd number is an odd number.

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