C :: Function That Computes Factorial Result Of Certain Number

I just want to practice in the language so i wrote this simple function that computes the factorial result of a certain number. The problem is that for all numbers > 20, the results are wrong ( < 20 all good).

I already learned that normal "long" type in c is more like 32 bit int and not 64 bit like a long type in java. so I used here a "long long" type.

why am I getting strange results above the number 20? isn't 64 bit enough to hold those numbers?

Code:
long long factorial(int n);
int main() {
long long result = factorial(20);
printf("%lld",result);

[code] ...

for 21 i get: -4249290049419214848

where the right result shoud be: 51,090,942,171,709,440,000