Number of zeros in a factorial number

[lauramaria]

It is given an integer "p". I have to find a number "n" for which "n factorial" has "p" numbers of zero at the end. Here is the solution i thought, but i am not sure if it is a solution for this problem. Do i have to make a function to calculate the factorial and another function to get the zeros?

int p;
int count5=0;
int i;
int copy_i;

printf("Enter p: ");
scanf("%d",&p);

for(i=1; ;i++)
{
    copy_i=i;

    while(copy_i/5)
    {
        if(copy_i%5==0)
        {
            count5++;
            copy_i=copy_i/5;
        }
        else
        {
            break;
        }
    }

    if(count5==p)
    {
        printf("The minimum number n is: %d.",i);
        break;
    }
    else if(count5>p) 
    {
        printf("No match for n! with %d zero.",p);
        break;
    }

}

[donbock]

Factorials get very big very fast. n! becomes too big to be represented in a C variable for depressingly small values of n. Besides that, a program to compute factorials can run disappointingly slow as n increases. Thus, I suggest you look for some alternative to the brute force algorithm suggested in your original post.

If a number ends in p zeroes, then it must be true that the number is divisible by 10^p. Find a list of distinct factors of 10^p and the largest value in that list will be the value n that you are looking for. Spend a lot of pencil-and-paper time to make sure your algorithm is correct before you write any code.