[解题报告]160 - Factors and Factorials

 Factors and Factorials 

The factorial of a number N (written N!) is defined as the product of all the integers from 1 to N. It is often defined recursively as follows:

 

 

 

 

Factorials grow very rapidly--5! = 120, 10! = 3,628,800. One way of specifying such large numbers is by specifying the number of times each prime number occurs in it, thus 825 could be specified as (0 1 2 0 1) meaning no twos, 1 three, 2 fives, no sevens and 1 eleven.

 

Write a program that will read in a number N (  ) and write out its factorial in terms of the numbers of the primes it contains.

 

Input

Input will consist of a series of lines, each line containing a single integer N. The file will be terminated by a line consisting of a single 0.

 

Output

Output will consist of a series of blocks of lines, one block for each line of the input. Each block will start with the number N, right justified in a field of width 3, and the characters `!', space, and `='. This will be followed by a list of the number of times each prime number occurs in N!.

These should be right justified in fields of width 3 and each line (except the last of a block, which may be shorter) should contain fifteen numbers. Any lines after the first should be indented. Follow the layout of the example shown below exactly.

 

Sample input

 

5
53
0

 

Sample output

 

  5! =  3  1  1
 53! = 49 23 12  8  4  4  3  2  2  1  1  1  1  1  1
        1



质因数处理会很麻烦，所以要把100以内质数找出来

#include<stdio.h>
#include<math.h>
main()
{
 int math[25]={0};
 int a,b,c,n,set=1;
 math[0]=2;
 for(a=3;a<100;a++)
  {
   int flag=0;
   for(b=2;b<=(int)sqrt(a);b++)
    if(a%b==0) {flag=1;break;}
   if(flag==0)
    {
     math[set]=a;
     set++;
    }
  }
 while(scanf("%d",&n)==1&&n!=0)
  {
   int temp[25]={0},max=0,maxset;
   printf("%3d! =",n);
   for(a=2;a<=n;a++)
    {
     int temp1=a;
     for(b=0;b<set;b++)
      {
       while(temp1%math[b]==0)
        {
         temp[b]++;
         temp1=temp1/math[b];
         if(math[b]>max)
          {max=math[b];maxset=b;}
         if(temp1==1) break;
        }
      }
    }
    int time=0,temp1=maxset+1;
    for(a=0;a<=maxset;a++)
     {
     time++;
     printf("%3d",temp[a]);
     if(time==15&&temp1>15)
      {
       time=0;
       temp1=temp1-15;
       printf("\n      ");
      }
     }
     printf("\n");
  }
 return 0;
}