an algorithm to calculate factorial " x! = ? " in C

Why does my code work correctly only when 12>=a ??

int main()
{
    int a ,x = 1;
    scanf("%d", &a);
    
    while (1 < a){
        x = a * x;
        a = (a - 1);
        printf("\n %d", x);
    };

    printf("\n %d", x);
    return 0;
}

what i did is asking the pc to print the result of a*(a-1) in every line then it prints the final factorial result.
And yes , the result is correct but not in all cases (from 13 and above it becomes wrong)

>Solution :

It is because factorial of 13 is greater than the holding capacity of int. So it cannot hold this value. try to use long variable here