Last updated on July 5th, 2025
If any numbers divisible by 2, they are called even numbers. These numbers help to count and divide items equally and play an essential role in mathematics and everyday life. In this topic, we will explore even numbers, their concepts, and properties in detail.
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.
Even Numbers | Odd Numbers |
Even numbers are evenly divisible by 2. For example, 4 ÷ 2 Quotient = 2 Remainder = 0 |
Odd numbers are not precisely divisible by 2, as they leave a remainder of 1. For example, 5 ÷ 2 Quotient = 2 Remainder = 1 |
0, 2, 4, 6, or 8 can be the last digit of an even number. | 1, 3, 5, 7, or 9 can be the last digit of an odd number. |
0, 2, 4, 6, or 8 can be the last digit of an even number. | 1, 3, 5, 7, or 9 can be the last digit of an odd number. |
12, 14, 16, 18, and 20 are a few examples of even numbers. | 11, 13, 15, 17, and 19 are a few examples of odd numbers. |
Even numbers can be paired into equal groups. |
Odd numbers cannot be paired in a group of 2; one remains as a leftover. |
The product of multiplying two even numbers is even. It is represented by 2n (2 × n = even number) n can be any integer: positive number (1, 2, 3…), negative numbers (-1, -2, -3…), or zero. |
The result of 2n + 1 is an odd number. |
We can find even numbers using various methods.
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:
Even numbers can be exactly divided by 2 without a remainder. For example, 62 ÷ 2 = 31 (with the remainder 0).
Understanding the properties and concept of even numbers helps us group items equally and make fair distributions. However, students make some mistakes when they deal with even numbers. Here are some common errors and helpful solutions to avoid them
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:
Which of the following numbers are even? 56, 39, 22, 65, 90, 71
The even numbers from the given list are 56, 22, and 90.
A number is even if its last digit is 0, 2, 4, 6, or 8.
Now we can list the even numbers:
56 → Ends in 6 (even)
39 → Ends in 9 (odd)
22 → Ends in 2 (even)
65 → Ends in 5 (odd)
90 → Ends in 0 (even)
71 → Ends in 1 (odd)
56, 22, and 90 are the even numbers from the given lis
Find the sum of the even numbers: 26, 54, 88.
168
First, we must add the first two numbers
26 + 54 = 80
Next, add the third number:
80 + 88 = 168
Thus, the sum of the even numbers 26, 54, and 88 is 168.
Mary had 32 oranges. She gave away 15 oranges. Does she have an even number of oranges left?
No, Mary does not have an even number of oranges left.
Mary had 32 oranges at first. She gave away 15 oranges. To find out how many oranges she has left, we subtract:
32 - 15 = 17
Here, 17 is the answer.
To determine whether 17 is an even number, we can check the last digit of the obtained answer.
A number is even if its last digit is 0, 2, 4, 6, or 8.
Hence, 17 is not an even number.
Thus, she has an odd number of oranges (17).
Allen had 48 books on his shelf. He removed 22 books. Will the remaining number of books be even?
Yes, the remaining number of books (26) is an even number.
Allen had 48 books.
Then he removed 22 books from the shelf.
So, we must determine if the remaining number of books is even.
For that, we must subtract:
48 − 22 = 26
There are 26 books left.
Next, we can check if 26 is an even number.
If a number ends in 0, 2, 4, 6, or 8 and is divisible by 2, it is considered even.
The number 26 ends in 6, which means it is even.
How many even numbers are there between 10 and 30?
There are 11 even numbers between 10 and 30, including 10 and 30.
Even numbers are those that are divisible by 2. The even numbers between 10 and 30 are:
10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
There are 11 even numbers.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.