## What Are Even Numbers?

**Even numbers are the numbers that are evenly divisible by 2.** **When divided by 2, even numbers leave a remainder of 0. Even numbers always end with 0, 2, 4, 6, or 8.**

Even numbers can be easily divided into equal groups. How? Let’s see! Can you count the number of kids and tell me if you can divide them equally among 2 teams?

There are 4 kids. They can be easily divided into two equal teams since 4 is an even number.

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## Even Numbers: Definition

**Even numbers are numbers ****divisible**** by “2.” The numbers that have the digits “0,” “2,” “4,” “6,” or “8” in the ones place are even numbers.**

**Even numbers examples: **22, 56, 98, 2, -16, 452, -867454, 12, 5752452, -98534, etc.

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## How to Identify Even Numbers

To identify even numbers, we observe the last digit or the ones digit of the number. If it ends in the digits **0, 2, 4, 6, or 8**, then it is an even number. Otherwise, it is an odd number.

**Example 1: 248**

Hundreds | Tens | Ones |
---|---|---|

2 | 4 | 8 |

Even Number |

**Example 2: 103**

Hundreds | Tens | Ones |
---|---|---|

1 | 0 | 3 |

Odd Number |

Another way is to divide the number by 2. If the remainder is “0,” then it is an even number; if the remainder is 1, then it is an odd number.

**Example 1:** $\frac{72}{2} = 36$ and remainder $= 0$

Thus, 72 is an even number.

**Example 2:** $\frac{35}{2} = 17$ R 1 since $(17 \times 2) + 1 = 35$

Thus, 35 is an odd number.

## Even Numbers on a Number Line

On a number line, if you start from 0 and keep taking jumps of 2, you will land on 2, 4, 6, 8, 10, and so on. These are even numbers.

If you make the jumps of 2 to the left of 0, you will meet the negative integers that are even. Notice that between two even numbers, there’s an odd number!

## General Form of an Even Number

Let n be any integer, then even numbers can be expressed as 2n.

General form of even numbers $= 2$n n is an integer

For example, if $n = 3$, we get an even number 6.

For $n = \;-\;5$, we get an even number $\;-\;10$.

## List of Even Numbers up to 100

Even Numbers up to 100 | ||||

2 | 4 | 6 | 8 | 10 |

12 | 14 | 16 | 18 | 20 |

22 | 24 | 26 | 28 | 30 |

32 | 34 | 36 | 38 | 40 |

42 | 44 | 46 | 48 | 50 |

52 | 54 | 56 | 58 | 60 |

62 | 64 | 66 | 68 | 70 |

72 | 74 | 76 | 78 | 80 |

82 | 84 | 86 | 88 | 90 |

## Properties of Even Numbers

- Even number $+$ Odd number $=$ Odd number.

For example, $8 + 5 = 13$.

- Even number $+$ Even number $=$ Even number.

For example, $8 + 4 = 12$.

- Odd number $+$ Odd number $=$ Even number.

For example, $3 + 5 = 8$.

**Property of Subtraction:**

- Even number $-$ Odd number $=$ Odd number

For example, $8 \;-\; 5 = 3$.

- Even number $-$ Even number $=$ Even number

For example, $16 \;-\; 10 = 6$.

- Odd number $-$ Odd number $=$ Even number

For example, $13 \;-\; 5 = 8$.

We can summarize the addition and subtraction properties as follows:

Addition | Subtraction | Result |
---|---|---|

Even $+$ Even | Even $-$ Even | Even |

Even $+$ Odd | Even $-$ Odd | Odd |

Odd $+$ Even | Odd $-$ Even | Odd |

Odd $+$ Odd | Odd $-$ Odd | Even |

- Multiplying an even number and an odd number (and vice versa) always results in an even number.

For example, $5 \times 6 = 30$.

- Multiplying an even number with an even number always results in an even number.

For example, $6 \times 10 = 60$.

- Multiplying odd and odd always results in an odd number.

For example, $13 \times 5 = 65$.

Operation$(\times)$ | Result |
---|---|

Even $\times$ Even | Even |

Even $\times$ Odd | Even |

Odd $\times$ Even | Even |

Odd $\times$ Odd | Odd |

## Facts about Even Numbers

- 0 is neither an even number nor an odd number.
- The sum of two or more even numbers is always even.
- The product of two or more even numbers is always even.
- If you can form two equal groups of the given number, or form a “doubles fact,” it is an even number.

## Conclusion

In this article, we learned about even numbers, their properties, how to identify even numbers and the list of even numbers. Let’s solve a few examples and practice problems to understand this better.

## Solved Examples on Even Numbers

**1. Identify the even numbers from the given list.**

$23, \;8,\; 46,\; 81,\; \;-\; 96,\; 73,\; \;-\;11,\; 62,\; 33,\; 74$

**Solution:**

Even numbers are divisible by 2 and end in the digits “0”,”2″, “4”, “6” or “8”.

The even numbers here are $8 ,\; 46,\;\;-\;96,\; 62,\; 74$.

**2. Find the sum of even numbers between 50 and 60.**

**Solution: **

The even numbers that lie between 50 and 60 are as follows:

$52,\; 54,\; 56,\; 58$

$52 + 54 + 56 + 58 = 220$

Sum $= 220$

**3. Check whether the number of objects in the image are even or odd.**

**Solution: **

There are 11 apples.

11 apples cannot be divided into two equal groups. If we divide 11 by 2, the remainder is 1. One apple will be left over.

Thus, 11 is an odd number.

**4. What is the sum of the smallest and the largest three-digit even numbers?**

**Solution:**

The smallest three-digit even number $= 100$

The largest three-digit even number $= 998$

Sum of the numbers $= 100+ 998= 1098$

**5. The lengths of the sides of a triangle are consecutive even numbers. Find out what the length of the longest side is if the perimeter of the triangle is 24 units?**

**Solution: **

Let n be any positive number. Three consecutive even numbers can be represented as

$2n,\; 2n + 2,\; 2n + 4$

So, $2n,\; 2n + 2,$ & $2n + 4$ be the lengths of the triangle.

Perimeter of triangle $=$ Sum of all the sides

$\Rightarrow 24 = 2n + 2n + 2 + 2n + 4$

$\Rightarrow 24 = 6n + 6$

$\Rightarrow 6n = 18$

$\Rightarrow n = 18 \div 6$

$\Rightarrow n = 3$

Hence, the lengths of the sides are

$2n = 2 \times 3 = 6$

$2n + 2 = 2 \times 3 + 2 = 8$

$2n + 4 = 2 \times 3 + 4 = 10$

So, the length of the longest side is 10 units.

## Practice Problems on Even Numbers

## Even Numbers: Definition, Properties, List, Examples, Facts

### What are the three consecutive even numbers whose sum is 72?

Let the three consecutive even numbers be $2n, 2n + 2$,and $2n +4$.

Sum of the numbers $= 72$

$\Rightarrow 72 = 2n + 2n + 2 +2n +4$

$\Rightarrow 72 = 6n + 6$

$\Rightarrow 6n = 66$

$\Rightarrow n = 11$

Hence, the numbers are

$2n = 2 \times 11 = 22$

$2n + 2= 2 \times 11 + 2 = 24$

$2n + 4= 2 \times 11 + 4 = 26$

The three consecutive even numbers are 22, 24 and 26.

### Identify an even number.

100 is an even number since it ends with 0.

### What is the smallest positive even number?

The smallest positive even number is “2.”

### The number 0 is _______.

0 is an even number.

0 is not a positive number.

## Frequently Asked Questions about Even Numbers

**What is the divisibility rule for the numbers divisible by 2?**

A number is divisible by 2 if it has 0, 2, 4, 6, or 8 at the ones place.

**Is 1 an odd number?**

Yes, 1 is an odd number because it is not divisible by 2.

**What is the only even prime number?**

2 is the only prime number that’s even.

**What is the general form of odd numbers?**

To express an odd number, we use a formula that is expressed as 2n ± 1, where n ∈ N.

**Why is 0 called the whole number?**

**Can negative numbers be even?**

Yes, negative numbers can be even. Even numbers can be both negative or positive.

**Can even numbers be negative?**

Yes, even numbers can be positive or negative. We refer to the negative even numbers as negative even integers.