C Algorithm to find base system with the highest number of nulls in the end

Question

As title says, I have to find the base system of given number which has the highest number of nulls in the end. For example if I have number 100 000, the answer is 10, because in 10 system there is the highest amount of nulls. Answer for number 54 would be 3, because in 3 numeral system it looks like 2000 (the highest amount of nulls in the end). I've written a program which works fine, but the problem comes if the number exceeds maximum of integer. I have no idea how to fix it.

#include <stdio.h>
#define NUM 29040838157


int convert(int number, int system)
{
    int i=0;    

    while(number%system == 0)
    {
        i++;
        number/=system;
    }

    return i;
}

int main()
{   
    int i,max;
    int temp=0;

    for(i=2;i<=NUM;i++)
    {
        if(convert(NUM,i) >= temp)
        {
            max=i;
            temp = convert(NUM,max);
        }
    }

    printf("%d\n",max);
}

Solved.
It's wise to use unsigned long long int or represent number in an array.

Answer 1

For larger number, you should use data type which can store higher integer values too. I recommend unsigned long long

#define NUM 29040838157ULL //note the ULL here    

unsigned long long convert(unsigned long long number, unsigned long long system)
{
    int i=0;    

    while(number%system == 0)
    {
        i++;
        number/=system;
    }

    return i;
}

int main()
{   
    unsigned long long i,max;
    unsigned long long temp=0;

    for(i=2;i<=NUM;i++)
    {
        if(convert(NUM,i) >= temp)
        {
            max=i;
            temp = convert(NUM,max);
        }
    }

    printf("%llu\n",max);
}

And so on