An even number can be divided by two, while an odd number cannot be divided by two. They can be either favorable or unfavorable. Even and odd numbers are always in the center, and vice versa. You still search for the last digit to distinguish between odd and even numbers. The last digit of an even number is always 0, 2, 4, 6, or 8, whereas an odd number’s last digit is always 1, 3, 5, 7, or 9.

**Properties of Even and Odd Numbers**

The odd and even numbers have special and essential properties regarding algebraic and mathematical operations like addition, subtraction, and multiplication or division. Whenever we apply or use these algebraic operations to two even or odd numbers, we will invariably get an even or odd number. We always exclude division here because the division sometimes gives you the result in fractions or decimals while talking about special characteristics of these numbers.

- When we add or subtract two respective even numbers, the result is invariably an even number. For instance, 6 + 2 = 8, 6 – 2 = 4
- When we add or subtract a respective even number and an odd number, the result is invariably odd. For instance, 7 + 2 = 9, 7 – 2 = 5
- When we add or subtract two odd numbers, the result is invariably an even number. For instance, 7 + 1 = 8, 7 – 1 = 6
- When we multiply two even numbers, the result is invariably an even number. For instance, 6 × 2 = 12
- When we multiply an even number and an odd number, the result is invariably an even number. For instance, 7 × 2 = 14
- When we multiply two odd numbers, the result is invariably an odd number. For instance, 7 × 1 = 7

**How to Identify a Number is Even or Odd?**

You must check the number in one’s (or unit’s) position to determine if the given number is odd or even. If you put the number in your spot, it will tell you if the number is odd or even. Consider the numbers 3, 845, 917, which all end in an odd number, such as 3, 5, and 7. As a result, the given numbers 3, 845, 917 are odd. As a result, the number is not even.

**By Comprehending the Number at “ones” Place**

In this method, we examine the number in the “ones” position of an integer to determine if it is even or odd. All of the numbers that end in 1,3,5,7, and 9 are odd. Odd numbers include numbers like 11, 23, 35, 47, and so on. Even numbers include those that end in 0,2,4,6, and 8. Even numbers, for example, include 14, 26, 32, 40, and 88.

**By Grouping**

- As two equal groups: When a number is divided into two classes, each with an equal number of elements, the result is an even number. When we group odd numbers together, we get a 1 as a remainder.
- As groups of “two” in each: It is an even number if it can be divided into several classes of “two” without leaving any remainder. A number is an odd number in the case of a remainder.

**Application of Even and Odd Numbers**

In later grades, number sense skills are useful for studying math, science, and communication systems. We use logic gates and binary codes to implement the principle in circuit design. Learning geometric shapes in ancient mathematics began with categorizing them as even or odd depending on the number of sides. Even and odd numbers are a very important and vital concept for students to understand. It forms the basis of mathematics and has many sub-topics related to even and odd numbers.