1.

/**
 * FWP, Ausgewählte Probleme aus dem ACM Programming Contest, SS10 
 * Problem: 10061 How many zero's and how many digits ?
 * Link: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=100&page=show_problem&problem=1002
 * 
 * @author Anton Pavlushko, IBB7B,  
 * @version 1.0, 10/10/2010
 * 
 * Status : Accepted
 * Runtime: 0.300
 */

import java.io.*;
import java.util.*;
public class Main {
	public static void main(String[] args) throws IOException {
	    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	    String current_line, empty = "";
        long number, factorial, i, j, length, number_local, count;
        long primes [], counts [];
        long znak,count5,count5_already,multiply;
        StringTokenizer input_string;
        boolean status, at_least_one;
        double try_it, base_log;
        Map<Integer,Integer> mp_number=new HashMap<Integer,Integer>();
        Map<Integer,Integer> mp_factorial=new HashMap<Integer,Integer>();
        
	     try {
	         while ((current_line=in.readLine())!= null && !current_line.equals("0")) { 
	        	 input_string = new StringTokenizer(current_line);
	        	 factorial = Integer.parseInt(input_string.nextToken());
	        	 number = Integer.parseInt(input_string.nextToken());
	        	 
	        	 if (!mp_number.isEmpty()) mp_number.clear();
	        	 if (!mp_factorial.isEmpty()) mp_factorial.clear();

	        	 number_local=number;
        		 length=number_local/2+1;
        		 at_least_one=false;
        		 for(j=2;j<=length;j++) {
        			 count=0;
        			 while(number_local%j==0) {
        				number_local=number_local/j;
        				count++;
        			 }
        			 
        			 if (count>0) {
       					 mp_number.put((int)j,(int)count);
        				 at_least_one=true;
        			 }
        			 
        			 if (number_local==1) break;
        		 }
	        	 
        		 if (at_least_one==false) {
        			 mp_number.put((int)number_local,1);
        		 }//it was prime
	        	 
        		 count=0;
	        	 for(Map.Entry<Integer,Integer> entry : mp_number.entrySet()) {
	        		 count=Math.max(count,entry.getValue());
//		        	 System.out.println(entry.getKey()+" - "+entry.getValue());
        		 }
//	        	 System.out.println(count);
	        	 
	        	 count=0;
	        	 for(Map.Entry<Integer,Integer> entry : mp_number.entrySet()) {
	        		 
		        	 znak=(int)Math.floor(Math.log10(factorial)/Math.log10(entry.getKey()));
		        	 if (factorial<=Math.pow(entry.getKey(),znak+1)) znak++; //2.999999999996 Problem...
		        	 
		        	 count5=0;
//		        	 System.out.println(znak+" : "+entry.getValue());
		        	 for(i=1;i<=znak;i++) {
		        		 count5_already=(int)Math.floor(factorial/Math.pow(entry.getKey(),i));
		        		 count5+=count5_already;
		        	 }
	        		 
		        	 mp_factorial.put((int)entry.getKey(),(int)count5);
		        	 
		        	 count=Math.max(count,count5);
//		        	 System.out.println(entry.getKey()+" - "+mp_factorial.get(entry.getKey()));
	        	 }

	        	 for(Map.Entry<Integer,Integer> entry : mp_number.entrySet()) {
	        		if (!mp_factorial.containsKey(entry.getKey())) { 
	        			count=0;
	        			break;
	        		}else{
//	   	        	 System.out.println(entry.getKey()+" - "+mp_factorial.get(entry.getKey())/entry.getValue());
	        			count=Math.min(count,mp_factorial.get(entry.getKey())/entry.getValue());
	        		}
        		 }
	        	 
	        	 if (true) { 
	        	 try_it=0;
	        	 base_log=Math.log10(number);
	        	 for(j=2;j<=factorial;j++) {
	        		 try_it+=Math.log10(j)/base_log;
        		 }
	        	 i=(int)Math.floor(try_it)+1;
	        	 } else if (false) {
	        		 try_it=Math.log10(Math.sqrt(2))/Math.log10(number)+0.00000001;
	        		 try_it+=Math.log10(Math.sqrt(Math.PI))/Math.log10(number)+0.00000001;
	        		 try_it+=Math.log10(Math.sqrt(factorial))/Math.log10(number)+0.00000001;
	        		 try_it+=factorial*(Math.log10(factorial/Math.E)/Math.log10(number)+0.00000001);
		        	 i=(int)Math.floor(try_it)+1;
	        	 }//Stirling...
	        	 
	        	 
	        	 System.out.println(count+" "+i);
	         } // end while 
	       } // end try
	       catch (IOException e) {
	         System.err.println("Error: " + e);
	       }
	}
}


2. 

/**
 * FWP:	Ausgewaehlte Probleme aus dem ACM (SS10)
 *
 * Method: Math: Primes
 * Problem: 10061 - HowManyZeros
 * Accepted: 0.256
 * @author Evgeni Pavlidis

 */
import java.io.*;
import java.util.*;

class Main {


    public static final int MAX = 800;
    public static final int[][] primeDivisor = new int[MAX+1][5];
    public static final int[][] primePower = new int[MAX+1][5];
    public static final int[] index = new int[MAX+1];

    
    private static void findBaseDivisors()
    {            
        int power,d;
        // sieve the multiples of 2
        for(int i = 2; i <= MAX; i+=2)
        {
            d = 2;
            power = 1;
            while((i % (d*2)) == 0)
            {
                d *= 2;    
                power++;
            }
            primePower[i][index[i]] = power;
            primeDivisor[i][index[i]++] = 2;
        }
            
        // sieve other numbers
        for(int i = 3; i <= MAX; i+=2)
            if(index[i] == 0)
                for(int j = i; j <= MAX; j += i)
                {
                    d = i;
                    power = 1;
                    while(j % (d*i) == 0)
                    {
                        d *= i;
                        power++;
                    }
                    primePower[j][index[j]] = power;
                    primeDivisor[j][index[j]++] = i;
                }
         
         /** /
         for(int i = 1; i <= MAX; i++)
            for(int j=0; j < index[i]; j++)
                System.out.println(i + " += " + primeDivisor[i][j]+"^" + primePower[i][j]);
         /**/
    }
    
    public static void main(String...args)
    {
        Scanner scanner = new Scanner(System.in);
        
        int n,b, digits, min, power = 0;
        long divisor;
        
        findBaseDivisors();
        
        while( scanner.hasNextInt() )
        {
            n = scanner.nextInt();
            b = scanner.nextInt();
            double digitsLogs = 0;
            
            min = Integer.MAX_VALUE;
            
            // calculate zeros         
            if(n == 0)
                min = 0;
            else
                for(int i = 0; i < index[b]; i++)
                {
                    power = 0;
                    divisor = 1;
                    
                    do
                    {

                        divisor *= primeDivisor[b][i];
                        //System.out.println("    " + n + "  " + divisor + " ==> " + n/divisor + " " + power);
                        power += n / divisor;
                    }
                    while( n / (divisor*primeDivisor[b][i]) > 0);
                    
                    //System.out.println(" ---- " + power + "  " + primePower[b][i]);
                    
                    
                    power = power / primePower[b][i];
                    
                    if(power < min)
                        min = power;
                }

            for(int i = 2; i <= n; i++)                
                digitsLogs += Math.log(i);
            digits = (int)Math.floor(digitsLogs/Math.log(b) + 1);
        
            System.out.println(((min < 0)? 0:min) + " " + digits); 
        }      
    }
}