Here's a solution for Java without having to convert to and from String or Character arrays:

int n = in.nextInt();
int r = n;
int count = 0;
while(r > 0){
    if(r % 10 != 0 && n % (r % 10) == 0) count++;
    r = r / 10;
}
System.out.println(count);

IMO it's a mistake to grant 25 points for such an easy challenge.

25 points? Seriously?

I dont understand. Why do people post their solutions here? Everybody wants to get recognition or something? Discussion is about giving hints that will help to solution, not posting your answers...

3 Lines of python. lololol.

for fluff in range(input()):
    value = int(raw_input())
    print len([i for i in map(int, list(str(value))) if i != 0 and value % i == 0])