1.
/**
* FWP, Ausgewählte Probleme aus dem ACM Programming Contest, WS10/11
* Problem: 10780 Again Prime? No Time.
* Link: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=19&page=show_problem&problem=1721
*
* @author Fabian Liebl
* @version 1.0, 10/06/2010
*
* Method : Ad-Hoc
* Status : Accepted
* Runtime: 0.324
*/

import java.io.*;

public class Main {

// Primes up to 5000
private static int[] prim = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107,
109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433,
439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521,
523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613,
617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887,
907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193,
1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291,
1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423,
1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601,
1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699,
1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029,
2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137,
2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459,
2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593,
2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693,
2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023,
3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167,
3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373,
3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607,
3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833,
3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931,
3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283,
4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423,
4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547,
4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789,
4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931,
4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999};

public static void main(String[] args) throws IOException {
BufferedReader inputReader = new BufferedReader(new InputStreamReader(System.in));

int testCases = Integer.parseInt(inputReader.readLine());
int m, n;
int temp1;
String[] input;

int[] primesInM = new int[prim.length];
int[] primesInMPower = new int[prim.length];
int[] primesInMCounters = new int[prim.length];
int numberOfPrimesInM;

for (int tc = 0; tc < testCases; tc++) {
System.out.println("Case " + (tc + 1) + ":");

input = inputReader.readLine().split(" ");
m = Integer.parseInt(input[0]);
n = Integer.parseInt(input[1]);

numberOfPrimesInM = 0;

// Factorize m
temp1 = m;
for (int i = 0; i < prim.length; i++) {
if (temp1 % prim[i] == 0) {
primesInM[numberOfPrimesInM] = prim[i];
primesInMPower[numberOfPrimesInM] = 0;
primesInMCounters[numberOfPrimesInM] = 0;
while (temp1 % prim[i] == 0) {
temp1 /= prim[i];
primesInMPower[numberOfPrimesInM] ++;
}
numberOfPrimesInM++;
if (temp1 == 1) break;
}
}

// Go through the factors of n
for (int i = 1; i <= n; i++) {
// How often can i be divided through m's factors
// Go through the factors
for (int f = 0; f < numberOfPrimesInM; f++) {
temp1 = i;
while (temp1 % primesInM[f] == 0) {
temp1 /= primesInM[f];
primesInMCounters[f] ++;
}
}
}

// Get the minimum number of counters (divided by the needed powers)
temp1 = primesInMCounters[0];
for (int f = 0; f < numberOfPrimesInM; f++) {
primesInMCounters[f] /= primesInMPower[f];
if (primesInMCounters[f] < temp1) {
temp1 = primesInMCounters[f];
}
}


if (temp1 == 0) {
// Not divisible
System.out.println("Impossible to divide");
} else {
System.out.println(temp1);
}
}
}

}


2.

/**
* FWP: Ausgewaehlte Probleme aus dem ACM (SS10)
*
* Method: number theory
* Problem: 10780 - Again Prime? No Time
* Accepted: 0.368
* @author Evgeni Pavlidis
*
*/

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

class Main {

public static final int MAX = 5000;
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;
}
}

public static void main(String...args)
{
Scanner scanner = new Scanner(System.in);

int testCases = scanner.nextInt();
int m, n, divisor, current;

findBaseDivisors();

for(int c = 1; c <= testCases; c++)
{
int result = Integer.MAX_VALUE;
m = scanner.nextInt();
n = scanner.nextInt();

for(int i = 0; i < index[m]; i++)
{
current = 0;
divisor = primeDivisor[m][i];

while( n / divisor > 0)
{
current += n / divisor;
divisor *= primeDivisor[m][i];
}

current = current / primePower[m][i];

if(current < result)
result = current;

}

System.out.printf("Case %d:\n", c);
if(result == 0)
System.out.println("Impossible to divide");
else
System.out.println(result);
}
}
}