Even Numbers 1 to 100 | Definition, Properties and Examples
Last Updated :
26 Sep, 2024
Ever wondered what even numbers are or how to define even in mathematics? Simply put, even numbers are those special numbers that can be divided by 2 without leaving a remainder. Numbers like 2, 4, 6, and 8 all fit this category. An even number is any number that can be expressed in the form: n = 2k, where k is an integer.
Understanding even numbers is crucial for mathematical literacy and for various applications in science, engineering, and everyday problem-solving.
Let's learn about even numbers from 1 to 100 in detail, including their properties and examples.
What are Even Numbers?
Even Numbers are those numbers that are exactly divisible by 2. This means that all even numbers are multiples of 2.
How to Identify Even Numbers
- Any number ending with digits 0, 2, 4, 6, and 8, is an Even Number, as all the numbers ending with digits 0, 2, 4, 6, and 8 are divisible by 2.
- Also, numbers ending with digits 1, 3, 5, 7, and 9 are odd numbers, as they are not divisible by 2 and give 1 as the remainder when divided by 2.
Here is the way you can know
- Numbers ending with 0, 2, 4, 6, and 8 are even numbers. Thus, 10880, 2314, and 23468 are even numbers.
- Numbers ending with 1, 3, 5, 7, and 9 are odd numbers. Thus, 16619 and 1923 are the odd numbers.
Smallest Even Number
Zero is the smallest even number. Zero is an integer and meets all the criteria for being even. It is neither positive nor negative but is considered an even number due to its divisibility by 2.
Even Numbers List From 1 to 100
Below is the list of even numbers from 1 to 100.
List of Even Numbers up to 100 |
|---|
2 | 22 | 42 | 62 | 82 |
4 | 24 | 44 | 64 | 84 |
6 | 26 | 46 | 66 | 86 |
8 | 28 | 48 | 68 | 88 |
10 | 30 | 50 | 70 | 90 |
12 | 32 | 52 | 72 | 92 |
14 | 34 | 54 | 74 | 94 |
16 | 36 | 56 | 76 | 96 |
18 | 38 | 58 | 78 | 98 |
20 | 40 | 60 | 80 | 100 |
Difference Between Even and Odd Numbers
Below is the difference between even and odd numbers:
Even Numbers | Odd Numbers |
|---|
Divisible by 2, remainder is 0. | Not divisible by 2, remainder is 1. |
|---|
2, 4, 6, 8, 10 (positive); -2, -4, -6, -8, -10 (negative) | 1, 3, 5, 7, 9 (positive); -1, -3, -5, -7, -9 (negative) |
|---|
2n, where n is an integer | 2n+1, where n is an integer |
|---|
Divisible by 2 | Not divisible by 2 |
|---|
Properties of Even Numbers
Let's learn some of the important properties of even numbers.
Divisibility by 2
The defining property of even numbers is that they are divisible by 2. For example, 8 ÷ 2 = 48 (an integer with no remainder).
Property of Even Number Addition
The sum of two even numbers is always even.
For example, 4 + 6 = 10
Here, 4 and 6 are even numbers and there sum i.e. 10 is also even.
Property of Even Number Subtraction
The difference between two even numbers is also always even.
For example, 8 − 4 = 4.
Here, 8 and 4 are even numbers and there difference i.e. 4 is also even.
Property of Even Number Multiplication
- The product of two even numbers is always even.
- The product of an even number and an odd number is also even.
Below is a table illustrating all the properties of even number along with an example:
| Operation | Example | Result |
|---|
| Even + Even | 4 + 2 | Even |
| Odd + Odd | 3 + 5 | Even |
| Even + Odd | 4 + 3 | Odd |
| Even - Even | 6 - 2 | Even |
| Odd - Odd | 7 - 5 | Even |
| Even - Odd | 6 - 3 | Odd |
| Odd - Even | 5 - 2 | Odd |
| Even × Even | 4 × 2 | Even |
| Even × Odd | 4 × 3 | Even |
| Odd × Even | 3 × 2 | Even |
| Odd × Odd | 3 × 3 | Odd |
Even Numbers on Number Line
Even numbers can be easily represented on the number line. They are represented by skipping one number and marking the other number starting from any even number.
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Consecutive Even Numbers
Consecutive even numbers are the even numbers that have a difference of 2 between any two numbers that come to one another.
Suppose we write, 6, 8, 10, and 12 then it is considered to be a consecutive even number and if the even number is written as, 4, 8, 14 then they are not considered to be a consecutive even number.
Even Natural Numbers
Natural numbers that are also even numbers are called even natural numbers.
Some examples of even natural are 2, 8, 14, 18, etc.
Even Numbers that are Prime
For any number to be a Prime Number, it's factors should be 1 and the number itself. All even numbers have 2 as their factor, therefore they can't be prime.
But there is one exception to this rule as 2 is the prime as well as even number.
Thus, 2 is the only even number that is prime as well.
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Even Numbers Solved Examples
Here are some solved examples on Even Numbers :
Example 1: Write any 10 consecutive even numbers between 1 and 50.
Solution:
As, every other number in a continuous series of natural numbers is even number.
So, 2, 4, 6, 8, 10, . . ., 48, 50 is the list of all even numbers between 1 and 50.
Thus, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 or 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 or 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 are some of the examples of 10 consecutive even numbers between 1 and 50.
Example 2: How many even numbers are between 1 and 300?
Solution:
Out of all integers, half of them are even and half of them are odd. So, there are 300 integers between 1 and 300 (including 1 and 300), so half of them are odd and half of them are even.
Thus, there are 150 even numbers between 1 and 300.
Example 3: What is the even natural number that can be written as the sum of two odd primes?
Solution:
The sum of two odd numbers is always even. Therefore, the smallest even number that can be written as the sum of two odd primes is 8.
The smallest two odd primes are 3 and 5. Their sum is 8, which is also even.
Therefore, the smallest even number that can be written as the sum of two odd primes is 8.
Example 4: Find the sum even numbers from 10 to 20.
Solution:
Even Numbers from 10 to 20 are 12, 14, 16, 18
Sum = 12 + 14 + 16 + 18
Sum = 60
Thus, the sum of even numbers from 10 to 20 is 60
Practice Problems on Even Numbers
Here are some practice questions on even numbers 1 to 100 for you to solve:
1. Find the sum of even numbers from 20 to 40
2. Check if the number given are even numbers or not, 78, 23, 46, 90.
3. Find the product of 12 and 24.
4. How many even numbers are their from 50 to 100?
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