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Maths

# What Are Even Numbers? | Definition, Properties, Solved Examples

Written by Prerit Jain

Updated on: 23 May 2023

### What Are Even Numbers? | Definition, Properties, Solved Examples

Do you get confused by odd and even numbers? But not anymore. If a number is a multiple of 2, then it’s an even number. However, if it’s not a multiple of 2, then it’s an odd number. In this article, you will read about even numbers: the best way to identify them, their types, and with solved examples.

## What are even numbers?

A number that is completely divisible by 2 is known as an even number.

Examples of even numbers are 2, 60, 94, etc.,

2 ÷ 2 = 1, Remainder = 0
60 ÷ 2 = 30, Remainder = 0
94 ÷ 2 = 47, Remainder = 0

Some of the quick ways to find an even number are:

• If a number can be divided into two equal parts, then it’s an even number.
• If a number does not leave any remainder after dividing by 2, then it’s an even number.
• If the number ends with 0, 2, 4, 6, or 8, then it’s an even number.

Try Yourself: Let’s assume you have 4 candies and try to guess if it’s an odd number or an even number. If you can divide 4 candies into 2 equal parts, then it’s an even number. If not, then it’s an odd number.

## Properties of even numbers

There are three major properties of even numbers that every student must know. These properties are the addition, subtraction, and multiplication of even numbers with an even number.

### Addition of two even numbers

When we add two even numbers then the result is an Even Number.

For example:

• 2 + 2 = 4
• 6 + 4 = 10
• 10 + 14 = 24

Try Yourself:

• 8 + 4 = ?
• 20 + 2 = ?
• 16 + 4 = ?

### Subtraction of two even numbers

When we subtract two even numbers then the result is an Even Number.

For example:

• 4 – 2 = 2
• 8 – 4 = 4
• 14 – 12 = 2

Try Yourself:

• 10 – 2 = ?
• 12 – 4 =?
• 10 – 4 =?

### Multiplication of two even numbers

When we multiply two even numbers then the result is an Even Number.

For example:

• 4 x 2 = 8
• 8 x 4 = 32
• 2 x 12 = 24

Try Yourself:

• 10 x 2 = ?
• 12 x 4 = ?
• 14 x 4 = ?

## Even Number List 1 to 1000

The even numbers from 1 to 1000 are tabulated below:

## Solved Examples

It’s time to learn more about even numbers with the help of some examples and practice questions. Hence, to help you with it, we have listed out some even numbers of solved examples here. First, try to solve the questions listed below on your own with your understanding and then see the solution.

Example 1: Identify if the 3608 number is an even number or not.
Solution:

3608 is an even number because when we divide it by 2, it will give 0 as a remainder.
3608 ÷ 2 = ?
3608 ÷ 2 = 1804
Quotient = 1804
Remainder = 0
If the remainder is 0, then the given number is an even number.

Example 2: Which of the following numbers are even numbers:
3, 50, 7, 94, 12, 15, 19, and 18?
Solution:
From the above, 50, 94, 12, and 18 are the only even numbers.
When the numbers 50, 94, 12, and 18 are divided by 2, the remainder is 0. However, when the numbers 3, 7, 15, and 19 are divided by 2, the remainder is 1.
Hence, those numbers which leave a remainder of 0 when divided by 2 are known as even numbers.

Example 3: What is the formula to find the sum of even numbers?
Solution: The formula to find the sum of Even Numbers is n * (n + 1).
Let’s find sum of first 5 even numbers = 5 * (5 +1)
= 5 * 6
= 30.
The sum of the first 5 Even numbers is 30.

Example 4: What is the Sum of the first 15 Even Numbers?
Solution: First 15 even numbers = 2, 4, 6, 8, and 10.
Sum of first 15 Even Numbers = n * (n + 1)
= 15 * (15 + 1)
= 15 * 16
= 240
The sum of the first 15 even numbers is 240.

## FAQs

How to identify even numbers?
If a number is divisible into two equal parts, then it’s an even number. There is a trick to identifying it without doing the actual division. Just look at the ones or end digits of the number. If the end digit is an even number like 0, 2, 4, 6, or 8, then the entire number is an even number.

What is the smallest even number?
2 is the smallest even number.

3580 is an even number?
Yes, 3580 is an even number. Because when we divide 3580 by 2, we get 0 as a remainder.

What is an even prime number?
2 is an even prime number. It’s the only even number that is a prime number. The fact is that, except for 2, all prime numbers are odd numbers.

What is the product of two even numbers?
The product of two even numbers is also going to be an even number. Furthermore, if you multiply an even number by an odd number, the result will be an even number.

To get better at maths, students must learn to identify even numbers. There are a few shortcuts or tricks you can learn and use to quickly identify even numbers. For example, if the end digit of a number is even, then the entire number is an even number.

In addition, the most common question related to even numbers is finding their sum. So, students don’t need to calculate them one by one but use the formula. The n * (n + 1) formula will help students find the sum of the first even number in the list. Keep in mind that it only calculates the first given number and not any random even number.

Written by by

Prerit Jain

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