zoj 1850 Factovisors

 

Factovisors
Time Limit: 1 Second      Memory Limit: 32768 KB
The factorial function, n! is defined thus for n a non-negative integer: 

0! = 1
n! = n * (n - 1)! (n > 0)

We say that a divides b if there exists an integer k such that 

k * a = b

Input

The input to your program consists of several lines, each containing two non-negative integers, n and m, both less than 2^31.

Output

For each input line, output a line stating whether or not m divides n!, in the format shown below.

Sample Input

6 9
6 27
20 10000
20 100000
1000 1009

Sample Output

9 divides 6!
27 does not divide 6!
10000 divides 20!
100000 does not divide 20!
1009 does not divide 1000!

 

Source: University of Waterloo Local Contest 1999.01.31

 

求m是否能整除n!
其实原理也很简单
首先将所有的质数（16位里面的正整数）筛选出来，推荐用素数筛选法
接着就是质数分解，将m的质数分解，并且得到质数表和质数的个数
接着按照得到的质数表，对n!的阶乘进行寻找相应质数的个数，看是否多余m中的质数的个数，以此判断即可
代码不贴了，比较丑陋