给定n，a求最大的k，使n！可以被a^k整除但不能被a^(k+1)整除。

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cmath>
 4 using namespace std;
 5 int su[168] = {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};
 6 int main()
 7 {
 8     int n,a;
 9     while(cin>>n>>a){
10         int an[168];
11         for(int i=0;i<168;i++){
12             an[i]=0;
13         }
14         //fenjie n!
15         for(int i=n;i>=0;i--){
16             int index=0;
17             int tmp=i;
18             while(tmp>=2){
19                 if(tmp%su[index]==0){
20                     tmp/=su[index];
21                     an[index]++;
22                 }
23                 else{
24                     index++;
25                 }
26             }
27         }
28         int bn[168];
29         for(int i=0;i<168;i++){
30             bn[i]=0;
31         }
32         //fenjie a
33         int t=a;
34         int index=0;
35         while(t>=2){
36             if(t%su[index]==0){
37                 t/=su[index];
38                 bn[index]++;
39             }
40             else{
41                 index++;
42             }
43         }
44         double minn=100000;
45         for(int i=0;i<168;i++){
46             if(bn[i]!=0){
47                 double f=an[i]/bn[i];
48                 if(f<minn){
49                     minn=f;
50                 }
51             }
52         }
53         cout<<int(minn+0.5)<<endl;
54     }
55     return 0;
56 }