by Yogi P - December 4, 2023

What is Even Number?

An even number is a type of integer that can be exactly divided by 2 without leaving any remainder. In simpler terms, if you divide an even number by 2, the result is always a whole number.

This is the defining characteristic that separates even numbers from odd numbers, which cannot be evenly divided by 2.

Defining an Even Number

An even number is any integer divisible evenly by 2, ending with 0, 2, 4, 6, or 8. Notable examples are 2, 4, 6, and 8. The smallest positive even and natural number is 2. In contrast, numbers not divisible by 2, such as 1, 3, 5, are known as odd numbers.

Distinguishing Between Even and Odd Numbers

All numbers fall into either the even or odd category. Identifying an even number is straightforward look at the unit’s digit. If a number ends in 0, 2, 4, 6, or 8, it is even number. For example, a number like 322 (ending with 2) is even, while number like 917 (ending with 7) is odd.

Distinguishing between even and odd numbers can be effectively illustrated in a tabular form:

This table outlines the primary characteristics and arithmetic properties of even and odd numbers, providing a clear and concise reference for differentiating between them

How to Know If any Number is Even or Odd?

To determine whether a number is even or odd, you can look at its unit digit, which is the rightmost digit in the number. Here’s a simple rule to follow:

1. Even Numbers: If the unit digit of a number is 0, 2, 4, 6, or 8, then the number is even. This is because even numbers are divisible by 2 without leaving any remainder. For example, numbers like 22, 48, and 70 are even because their unit digits (2, 8, and 0, respectively) are among these specified digits.
2. Odd Numbers: Conversely, if the unit digit is 1, 3, 5, 7, or 9, the number is odd. Odd numbers are not divisible by 2 evenly; they leave a remainder of 1 when divided by 2. For instance, 15, 37, and 59 are odd numbers as their unit digits are 5, 7, and 9, respectively.

This method works for all integers, regardless of their size, and is a quick and effective way to classify numbers as either even or odd.

List of Even Numbers up to 100

Here is a list of even numbers from 2 up to 100:

Each of these numbers is divisible by 2 without leaving a remainder, which defines them as even numbers.

Properties of Even Numbers

The properties of even numbers can be summarized in a tabular format, focusing on the operations of addition, subtraction, and multiplication:

These properties illustrate the basic arithmetic behaviors of even numbers and can be used to predict the results of calculations involving them.

Property of Addition

The property of addition for even and odd numbers can be summarized as follows:

1. Adding Two Even Numbers: The sum of two even numbers is always an even number. This is because each even number is a multiple of 2, and the sum of two multiples of 2 is also a multiple of 2. For example, 4 + 6 = 10, and 10 is an even number.
2. Adding Two Odd Numbers: The sum of two odd numbers is always an even number. Odd numbers are one more (or one less) than an even number, so adding them together is like adding two even numbers and then adding 2 (which is even). For instance, 3 + 5 = 8, and 8 is an even number.
3. Adding an Even and an Odd Number: The sum of an even and an odd number is always odd. Since an odd number is an even number plus 1, adding an even number to it essentially adds an extra 1 to the sum, making it odd. For example, 4 (even) + 3 (odd) = 7, and 7 is an odd number.

Property of Subtraction

The property of subtraction for even and odd numbers can be outlined as follows:

1. Subtracting Two Even Numbers: The difference between two even numbers is always even. This is because each even number can be expressed as a multiple of 2, and the subtraction of two such multiples results in another multiple of 2. For example, 8 – 2 = 6, and 6 is an even number.
2. Subtracting Two Odd Numbers: The difference between two odd numbers is always even. Similar to the even case, since odd numbers are one more (or one less) than an even number, subtracting them is akin to subtracting two even numbers. For instance, 9 – 5 = 4, and 4 is an even number.
3. Subtracting an Odd Number from an Even Number: The result is odd. When you subtract an odd number from an even number, it’s like subtracting an even number and then removing 1 more, which leads to an odd result. For example, 10 (even) – 3 (odd) = 7, and 7 is an odd number.
4. Subtracting an Even Number from an Odd Number: The result is odd. Since an odd number is one more than an even number, subtracting an even number from it leaves behind the extra 1, making the result odd. For instance, 7 (odd) – 4 (even) = 3, and 3 is an odd number.

Property of Multiplication

The property of multiplication for even and odd numbers can be described as follows:

1. Multiplying Two Even Numbers: The product of two even numbers is always even. Since each even number is a multiple of 2, multiplying them results in a number that is also a multiple of 2. For instance, 4 × 6 = 24, and 24 is an even number.
2. Multiplying Two Odd Numbers: The product of two odd numbers is always odd. This is because odd numbers can be represented as $2n+1$, where $n$ is an integer. When you multiply two such numbers, the result, according to algebra, will have an odd number as its last term, making the product odd. For example, 3 × 5 = 15, and 15 is an odd number.
3. Multiplying an Even and an Odd Number: The product of an even and an odd number is always even. Since the even number in the multiplication is a multiple of 2, and any number (odd or even) multiplied by 2 results in an even number, the product will be even. For instance, 4 (even) × 3 (odd) = 12, and 12 is an even number.

These properties are foundational in arithmetic and are crucial for understanding the outcomes of different operations involving even and odd numbers.

Solved problems on Even Numbers

Example 1

Is 48 an even number?

Solution:

Yes, 48 is an even number. Since it ends with 8 (an even digit), it is divisible by 2. (48 ÷ 2 = 24)

Example 2

Find the sum of the first three even numbers greater than 20.

Solution:

The first three even numbers greater than 20 are 22, 24, and 26. The sum is 22 + 24 + 26 = 72.

Example 3

If you multiply an even number by 5, will the result always be even?

Solution:

No, the result will be odd. Multiplying any number by 5 results in a number ending with 5 or 0. If the even number ends in 0, the result is even; if it ends in any other even digit, the result is odd.

Example 4

What is the product of the smallest even number and the largest single-digit even number?

Solution:

The smallest even number is 2, and the largest single-digit even number is 8. Their product is 2 × 8 = 16, which is an even number.

Example 5

How many even number / numbers are there between 1 and 10?

Solution:

The even numbers between 1 and 10 are 2, 4, 6, and 8. There are 4 even numbers in this range.

Worksheet on Even Numbers

Identify the Even Numbers:

Circle the even numbers in the following list:

13, 22, 35, 42, 57, 64, 79, 88, 93

True or False:

State whether following statements are true or false:

1. The sum of two even numbers is always an even number.
2. The sum of an even number and an odd number is an even number.
3. The product of two even numbers is always odd number.
4. Every even number is divisible by 4.

Fill in the Blanks:

1. The smallest positive even number is ____.
2. The next even number after 29 is ____.
3. 50 is an ____ (odd/even) number.

Problem Solving:

1. What is the even number immediately preceding 71?
2. If you add the even number 16 to an unknown number and the result is 30, what is the unknown number?
3. If you multiply an even number by 3, is the result always even?

Listing Even Numbers:

List all the even numbers between:

1. 15 and 25
2. 31 and 41
3. 50 and 70
4. 60 and 100

Even Number Properties:

1. If an even number is divided by 2, the quotient is ____.
2. The unit digit of an even number can be ____, ____, ____, ____, or ____.

Bonus Challenge:

• Find an even number that is a prime number.
• Is zero considered an even number? Explain your answer.

Frequently Asked Questions on Even Numbers

Q1.  What Is an Even Number in Mathematics?

• An even number is any integer that is exactly divisible by 2. It ends with 0, 2, 4, 6, or 8 in the unit’s place.

Q2.  Is 2 Considered an Even Number?

• Yes, 2 is an even number. It is the smallest and the only even prime number.

Q3.  What Are the Even Numbers Between 1 and 50?

• The even numbers between 1 and 50 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, and 50.

Q4.  Which Is the Only Even Prime Number?

• 2 is the only even prime number, as it is only divisible by 1 and itself.

Q5.  How Do You Write the General Form of an Even Number?

• The general form of an even number is expressed as 2n, where n is an integer.

Q6.  Is Zero (0) Considered an Even Number?

• Yes, zero is considered an even number because it is divisible by 2 and leaves a remainder of 0.

Q7.  Is 41 an Even Number?

• No, 41 is not an even number. It is an odd number because it leaves a remainder of 1 when divided by 2.

Q8.  What Are the Main Properties of Even Numbers?

• Main properties include: the sum of two even numbers is even; the sum of an even number and an odd number is odd; the product of two even numbers is even; and the product of an even number and an odd number is even.

Q9.  Can the Sum of Two Odd Numbers Be Even?

• Yes, the sum of two odd numbers is always even. For example, 3 + 5 = 8.

Q10. What Happens When You Multiply an Odd Number with an Even Number?

• Multiplying an odd number with an even number always results in an even number.

Summary: Even numbers are fundamental in mathematics and are used in various applications, from basic arithmetic to more complex concepts in algebra, number theory, and beyond. The smallest positive even number is 2, which is also the only even prime number.