Determining whether an integer is even or odd is a fundamental task in programming. This involves checking if the integer is divisible by 2 without leaving a remainder. Let’s break down the concept, provide an example, and show how to implement this in different programming languages.

### Understanding the Problem

An integer is classified as:

**Even**if it is divisible by 2 with no remainder. Mathematically, an integer ( n ) is even if ( n \% 2 = 0 ), where`%`

is the modulo operator.**Odd**if it is not divisible by 2 evenly. Mathematically, an integer ( n ) is odd if ( n \% 2 = 1 ) (or ( n \% 2 = -1 ) in some languages that handle negative numbers differently).

### Example

Consider the integer `7`

.

**Even Check**:

- ( 7 \% 2 = 1 )
- Since the result is not
`0`

,`7`

is odd.

Consider the integer `8`

.

**Even Check**:

- ( 8 \% 2 = 0 )
- Since the result is
`0`

,`8`

is even.

### Step-by-Step Approach

**Input**: Read or receive the integer.**Modulo Operation**: Use the modulo operator to find the remainder when the integer is divided by 2.**Check Remainder**:

- If the remainder is
`0`

, the integer is even. - If the remainder is
`1`

(or`-1`

depending on language), the integer is odd.

**Output**: Display or return whether the integer is even or odd.

### Code Examples

#### 1. Python

```
def check_even_odd(n):
if n % 2 == 0:
return "Even"
else:
return "Odd"
# Example usage
n = 7
print(f"The number {n} is:", check_even_odd(n))
n = 8
print(f"The number {n} is:", check_even_odd(n))
```

#### 2. JavaScript

```
function checkEvenOdd(n) {
if (n % 2 === 0) {
return "Even";
} else {
return "Odd";
}
}
// Example usage
let n = 7;
console.log(`The number ${n} is: ${checkEvenOdd(n)}`);
n = 8;
console.log(`The number ${n} is: ${checkEvenOdd(n)}`);
```

#### 3. Java

```
public class Main {
public static String checkEvenOdd(int n) {
if (n % 2 == 0) {
return "Even";
} else {
return "Odd";
}
}
public static void main(String[] args) {
int n = 7;
System.out.println("The number " + n + " is: " + checkEvenOdd(n));
n = 8;
System.out.println("The number " + n + " is: " + checkEvenOdd(n));
}
}
```

#### 4. C++

```
#include <iostream>
std::string checkEvenOdd(int n) {
if (n % 2 == 0) {
return "Even";
} else {
return "Odd";
}
}
int main() {
int n = 7;
std::cout << "The number " << n << " is: " << checkEvenOdd(n) << std::endl;
n = 8;
std::cout << "The number " << n << " is: " << checkEvenOdd(n) << std::endl;
return 0;
}
```

#### 5. C

```
using System;
class Program {
public static string CheckEvenOdd(int n) {
if (n % 2 == 0) {
return "Even";
} else {
return "Odd";
}
}
static void Main() {
int n = 7;
Console.WriteLine("The number " + n + " is: " + CheckEvenOdd(n));
n = 8;
Console.WriteLine("The number " + n + " is: " + CheckEvenOdd(n));
}
}
```

To determine if an integer is even or odd, you use the modulo operator to find the remainder when the integer is divided by 2. If the remainder is `0`

, the number is even; otherwise, it is odd. The provided code examples in Python, JavaScript, Java, C++, and C# demonstrate this concept using the syntax and features of each language. This simple check is a fundamental operation in programming and forms the basis for more complex algorithms and logic.