Introduction:

Prime factorization is the process of finding the prime numbers that multiply together to give the original number. For example, the prime factors of 12 are 2, 2, and 3, as 2 × 2 × 3 = 12. This concept is fundamental in mathematics and is used in many algorithms, including encryption techniques. In this program, we will find and display the prime factors of a given number.

Objective:

The objective of this program is to determine the prime factors of any positive integer inputted by the user. It will use an efficient method to find the factors and display them one by one.

Code:

#include 

// Function to find and print the prime factors of a number
void prime_factors(int n) {
    // Print the number of 2s that divide n
    while (n % 2 == 0) {
        printf("%d ", 2);
        n /= 2;
    }

    // n must be odd at this point, so a skip of 2 (i = i + 2) can be used
    for (int i = 3; i * i <= n; i += 2) { // While i divides n, print i and divide n by i while (n % i == 0) { printf("%d ", i); n /= i; } } // This condition is to handle the case when n is a prime number greater than 2 if (n > 2) {
        printf("%d ", n);
    }
}

int main() {
    int num;

    // Asking the user to input a number
    printf("Enter a number to find its prime factors: ");
    scanf("%d", &num);

    // Checking if the number is greater than 1
    if (num > 1) {
        printf("The prime factors of %d are: ", num);
        prime_factors(num);
    } else {
        printf("Please enter a number greater than 1.\n");
    }

    return 0;
}

Program Explanation:

The program is structured in the following way:

• prime_factors function: This function takes an integer ‘n’ as input and prints the prime factors of ‘n’. It first handles the factor of 2, then proceeds with odd numbers (starting from 3). If any number divides ‘n’, it is printed and ‘n’ is divided by that number until ‘n’ is no longer divisible by it.
• main function: The user is prompted to enter a number, which is then passed to the prime_factors function for calculation. If the input number is less than or equal to 1, the program asks the user to enter a valid number greater than 1.

How to Run the Program:

Follow these steps to run the program:

1. Copy the code into a C file, for example, prime_factors.c.
2. Open a terminal or command prompt.
3. Navigate to the directory where your C file is saved.
4. Compile the program using a C compiler by running the command:

   gcc prime_factors.c -o prime_factors

5. Run the compiled program by typing:

   ./prime_factors

6. Enter a number when prompted, and the program will display its prime factors.