Write a C program, using functions where the function calculates the factorial of a given integer, and the main() program does I/O and calling of factorial function.

Sure, here is a simple C program that calculates the factorial of a given integer using a function:

#include <stdio.h>

// Function to calculate factorial
long long factorial(int n) {
    if (n >= 1)
        return n*factorial(n-1);
    else
        return 1;
}

int main() {
    int num;
    printf("Enter a positive integer: ");
    scanf("%d",&num);
    if (num < 0)
        printf("Error! Factorial of a negative number doesn't exist.");
    else {
        printf("Factorial of %d = %lld", num, factorial(num));
    }
    return 0;
}

In this program, the factorial() function is used to calculate the factorial of a number. The main() function handles the input/output and calls the factorial() function. If the input number is less than 0, it will print an error message. Otherwise, it will print the factorial of the input number.