Calculating factorials is one of the most classic examples used in teaching recursion. The code to do so is quite simple:
int factorial(int i) {
if(i)
return i * factorial(i-1);
return 1;
}
The realistic problem with this is that factorials get really big, really fast. Only 13! is so large that it overflows a 32 bit int. Unless you're dealing with 64 bit numbers, it makes more sense to use a lookup table. The work just isn't worth it.
int factorial(int i) {
if (i<0 || i>12) {
fprintf(stderr, "Factorial input out of range\n");
exit(EXIT_FAILURE); // You could also return an error code like -1
}
static const int factorials[] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600};
return factorials[i];
}
If you need larger factorials, use a 64 bit number (long long or int64_t). You could still use a lookup table for improved performance.
I can't remember where I read this trick.