c - Why the infinite loop when data type is unsigned int?

Question

The below code runs perfectly.Gives the correct output but, the moment I change the sign of the variables from signed to unsigned the program runs into an infinite loop. The program is to find the factorial of integers. The value of any variable doesn't get negative anywhere I am aware of the modular behavior of the unsigned int.

#include<stdio.h>

int main(void)
{
    int a[200], i,index, number, next, count, temp, test, x;

    scanf(" %d", &test);

    while(test--)
    {
        scanf(" %d", &number);
        a[0]=1;
        count=1;    //1 digit
        for(next=2;next<=number;++next)
        {
            index=0;temp=0;
            for(i=0;i<count;++i)
            {
                x=a[index]*next+temp;
                a[index]=x%10;
                temp=x/10;
                ++index;
            }
            while(temp!=0)
            {
                a[count++]=temp%10;
                temp=temp/10;
            }
        }
        for(i=count-1;i>=0;--i)
        printf("%d",a[i]);
        printf("
");
    }
    return 0;
}

Answer 1

The problem is that,

for(i=count-1;i>=0;--i)

Will never exit if i is unsigned. Because i is unsigned it will always be greater than or equal to zero, and thus the loop can't end.