C Program To Determine Divisible Even And Odd Of 2 And 3

Divisibility rules are fundamental concepts in number theory and programming, enabling efficient categorization and manipulation of integers. In this article, you will learn how to implement C programs to determine if a number is even or odd, and simultaneously check its divisibility by 2 and 3.

Problem Statement

The challenge lies in writing C code that can accurately and efficiently classify an integer based on its parity (even or odd) and its divisibility by the numbers 2 and 3. This is crucial for tasks requiring conditional logic or number filtering, where specific properties of numbers need to be identified.

Example

Consider the number 18. A program would identify it as:

• Even
• Divisible by 2
• Divisible by 3
• Even and divisible by 3

Background & Knowledge Prerequisites

To understand and implement the solutions, readers should be familiar with:

• Basic C Syntax: Variable declaration, input/output operations using printf and scanf.
• Modulo Operator (%): This operator returns the remainder of a division. For example, 10 % 3 evaluates to 1.
• Conditional Statements: if, else if, and else statements for decision-making logic.
• Logical Operators: && (AND), || (OR) for combining multiple conditions.
• Standard Input/Output Library: Including for console operations.

Use Cases or Case Studies

Understanding how to check for divisibility by 2 and 3 has several practical applications:

• Number Filtering: In data processing, you might need to filter a list of numbers, keeping only those that are even and divisible by 3.
• Game Development: Simple games often use divisibility rules for scoring (e.g., points awarded if a number drawn is even or a multiple of 3).
• Educational Tools: Creating interactive programs to teach children about number properties and divisibility rules.
• Input Validation: Ensuring that user input meets specific numeric criteria, like requiring an even number or a multiple of three.
• Basic Cryptography/Hashing: Simple algorithms might use divisibility as part of their logic.

Solution Approaches

Here, we explore various methods to determine a number's divisibility by 2 and 3, along with its even/odd status.

Approach 1: Basic Modulo Checks for a Single Number

This approach directly applies the modulo operator to check for even/odd status and divisibility by 3 independently.

Summary: Determine if a number is even (divisible by 2) or odd, and separately check if it's divisible by 3 using the modulo operator.

// Basic Divisibility Checks
#include <stdio.h>

int main() {
    int number;

    // Step 1: Prompt user for input
    printf("Enter an integer: ");
    scanf("%d", &number);

    // Step 2: Check for even or odd
    if (number % 2 == 0) {
        printf("%d is an even number.\\n", number);
    } else {
        printf("%d is an odd number.\\n", number);
    }

    // Step 3: Check for divisibility by 2 (redundant if even/odd checked, but explicit)
    if (number % 2 == 0) {
        printf("%d is divisible by 2.\\n", number);
    } else {
        printf("%d is not divisible by 2.\\n", number);
    }

    // Step 4: Check for divisibility by 3
    if (number % 3 == 0) {
        printf("%d is divisible by 3.\\n", number);
    } else {
        printf("%d is not divisible by 3.\\n", number);
    }

    return 0;
}

Run

Sample Output:

Enter an integer: 18
18 is an even number.
18 is divisible by 2.
18 is divisible by 3.

Enter an integer: 7
7 is an odd number.
7 is not divisible by 2.
7 is not divisible by 3.

Stepwise Explanation:

1. The program takes an integer input from the user.
2. number % 2 == 0 checks if the remainder when number is divided by 2 is 0. If true, the number is even; otherwise, it's odd.
3. number % 3 == 0 checks if the remainder when number is divided by 3 is 0. If true, the number is divisible by 3.
4. Each check is performed independently using if-else statements.

Approach 2: Combining Checks with Logical Operators

This approach builds on the previous one by combining the divisibility checks using logical AND (&&) to identify numbers that satisfy multiple conditions simultaneously.

Summary: Use logical && to check if a number is both even/odd and divisible by 3 in a single conditional statement.

// Combined Divisibility Checks
#include <stdio.h>

int main() {
    int number;

    // Step 1: Prompt user for input
    printf("Enter an integer: ");
    scanf("%d", &number);

    // Step 2: Check for even and divisible by 3
    if (number % 2 == 0 && number % 3 == 0) {
        printf("%d is an even number and is divisible by 3.\\n", number);
    }
    // Step 3: Check for odd and divisible by 3
    else if (number % 2 != 0 && number % 3 == 0) {
        printf("%d is an odd number and is divisible by 3.\\n", number);
    }
    // Step 4: Check for even but not divisible by 3
    else if (number % 2 == 0 && number % 3 != 0) {
        printf("%d is an even number but not divisible by 3.\\n", number);
    }
    // Step 5: Check for odd and not divisible by 3
    else { // This covers number % 2 != 0 && number % 3 != 0
        printf("%d is an odd number and not divisible by 3.\\n", number);
    }

    return 0;
}

Run

Sample Output:

Enter an integer: 6
6 is an even number and is divisible by 3.

Enter an integer: 9
9 is an odd number and is divisible by 3.

Enter an integer: 10
10 is an even number but not divisible by 3.

Enter an integer: 7
7 is an odd number and not divisible by 3.

Stepwise Explanation:

1. The program takes an integer input.
2. It uses a series of if-else if-else statements to categorize the number.
3. Each if or else if condition combines two modulo checks using the logical AND operator (&&).

• number % 2 == 0 && number % 3 == 0: True if the number is even AND divisible by 3.
• number % 2 != 0 && number % 3 == 0: True if the number is odd AND divisible by 3.
• number % 2 == 0 && number % 3 != 0: True if the number is even AND not divisible by 3.

1. The final else block catches all other cases, which logically must be odd and not divisible by 3.

Approach 3: Using Functions for Reusability

For larger programs or when these checks need to be performed multiple times, encapsulating the logic within functions promotes reusability and improves code readability.

Summary: Define separate functions for checking even, odd, divisible by 2, and divisible by 3 to modularize the code.

// Functional Divisibility Checks
#include <stdio.h>
#include <stdbool.h> // For using bool type

// Function to check if a number is even
bool isEven(int num) {
    return (num % 2 == 0);
}

// Function to check if a number is odd
bool isOdd(int num) {
    return (num % 2 != 0);
}

// Function to check if a number is divisible by 3
bool isDivisibleBy3(int num) {
    return (num % 3 == 0);
}

int main() {
    int number;

    // Step 1: Prompt user for input
    printf("Enter an integer: ");
    scanf("%d", &number);

    // Step 2: Use functions to determine properties
    if (isEven(number)) {
        printf("%d is an even number.\\n", number);
    } else {
        printf("%d is an odd number.\\n", number);
    }

    if (isDivisibleBy3(number)) {
        printf("%d is divisible by 3.\\n", number);
    } else {
        printf("%d is not divisible by 3.\\n", number);
    }

    // Step 3: Combine functional checks
    if (isEven(number) && isDivisibleBy3(number)) {
        printf("%d is even and divisible by 3.\\n", number);
    } else if (isOdd(number) && isDivisibleBy3(number)) {
        printf("%d is odd and divisible by 3.\\n", number);
    } else if (isEven(number) && !isDivisibleBy3(number)) {
        printf("%d is even but not divisible by 3.\\n", number);
    } else { // isOdd(number) && !isDivisibleBy3(number)
        printf("%d is odd and not divisible by 3.\\n", number);
    }

    return 0;
}

Run

Sample Output:

Enter an integer: 12
12 is an even number.
12 is divisible by 3.
12 is even and divisible by 3.

Enter an integer: 5
5 is an odd number.
5 is not divisible by 3.
5 is odd and not divisible by 3.

Stepwise Explanation:

1. Three functions, isEven, isOdd, and isDivisibleBy3, are defined. Each takes an integer and returns true or false (from ) based on its respective check.
2. In main, after getting user input, these functions are called to determine the number's properties.
3. The if-else if-else structure then uses the return values of these functions, combined with logical operators, to categorize the number comprehensively.
4. This approach makes the main function cleaner and easier to read, as the detailed logic for each check is abstracted into dedicated functions.

Conclusion

Determining a number's parity and divisibility by specific integers like 2 and 3 are foundational skills in C programming. By mastering the modulo operator and conditional statements, whether through direct checks, combined logical operations, or modular functions, you can effectively categorize and process numbers according to these essential properties.

Summary

• The modulo operator (%) is key for checking divisibility; a remainder of 0 indicates divisibility.
• A number is even if number % 2 == 0; otherwise, it's odd.
• Logical operators (&&, ||) enable combining multiple divisibility conditions efficiently.
• Functions enhance code organization and reusability for repeated checks, making programs cleaner and more maintainable.
• These checks are vital for conditional logic, data filtering, and input validation in various applications.