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N!的质因子分解

Posted by liangkangqi at 2006-05-12 10:08:45 on Problem 1401
例如:
20!
1.先求出20以内的素数,(2,3,5,7,11,13,17,19)
2.再求各个素数的阶数
e(2)=[20/2]+[20/4]+[20/8]+[20/16]=18;
e(3)=[20/3]+[20/9]=8;
e(5)=[20/5]=4;
...
e(19)=[20/19]=1;

所以
N!=2^18*3^8*5^4*...*19^1
因此,如果要求N!后面有多少个0,只要求出有多少个5就行了.......

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