UVA 160-factors and Factorials

Factors and Factorials

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

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

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

Input

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

Output

Output would consist of a series of blocks of lines, one block for each line of the input. Each block would start with the number N, right justified in a field of width 3, and the characters '!', Space, an d '='. This'll 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 could be shorter) Shou LD contain fifteen numbers. Any lines after the first should is indented. Follow the layout of the example shown below exactly.

Sample Input

5530

Sample Output

  5! =  3  1  1 53! =  8  4  4  3  2  2  1  1  1  1  1  1        1

#include <cstdio> #include <cstring>using namespace Std;bool isprime (int a) {int i;for (i = 2; i*i <= a;i++) I F (a%i = = 0) return False;return true;} int prime[100], count[100];int main () {int N;int i,num;for (i = 2, num = 0; I <= 100;i++) if (IsPrime (i)) {prime[num++] = i;}  while (scanf ("%d", &n) = = 1 && N) {memset (count,0,sizeof (count)); int maxn = 0;for (i = 2; I <= n; i++) {int m = I;int J;for (j = 0; j < Num; J + +) {while (m%prime[j] = = 0) {m = m/prime[j];count[j]++;if (J>MAXN) MAXN = j;}}} printf ("%3d! = ", n); for (i = 0; I <= maxn; i++) {if (i = =) printf (" \ n      "); printf ("%3d ", Count[i]);} printf ("\ n");} return 0;}

This problem should pay particular attention to the output format.

UVA 160-factors and Factorials