Please try my program for different input data, I don't know where I am wrong. Maybe I missunderstood problem, everyone use array, I don't think it's necessary ?!

#include <iostream.h>
#include <math.h>

int main()
{
      int niz[10];
      int brojac = 1;
      int rezultat;
      int p = 1;
      int koren;
      for (int i = 0; i < 10; i++)
          cin >> niz[i];
      for (int j = 0; j < 10; j++)
          p = p * niz[j];
      if (p == 1)
      {
         cout <<1;
         return 0;
      }
      koren = floor(sqrt((double)p));

      for (int k = 2; k <=koren; k++)
      {
          if (p % k == 0)
          {
             if (p/k == k)
                brojac++;
             else
                 brojac = brojac + 2;
          }
      }
      brojac++;

          rezultat = brojac % 10;
          cout << rezultat;

      return 0;
}

What your answer for test:
10000
10000
10000
10000
10000
10000
10000
10000
10000
10000

For this test p=10^40.