[数论] HOJ 1528/ZOJ 1823 Factoring Large Numbers

传送门：Factoring Large Numbers

Factoring Large Numbers
Time Limit: 2 Seconds      Memory Limit: 65536 KB
One of the central idea behind much cryptography is that factoring large numbers is computationally intensive. In this context one might use a 100 digit number that was a product of
two 50 digit prime numbers. Even with the fastest projected computers this factorization will take hundreds of years.

You don't have those computers available, but if you are clever you can still factor fairly large numbers.

Input
The input will be a sequence of integer values, one per line, terminated by a negative number. The numbers will fit in gcc's long long int datatype.

Output
Each positive number from the input must be factored and all factors (other than 1) printed out. The factors must be printed in ascending order, and followed by a single blank line.

Sample Input

90

1234567891

18991325453139

12745267386521023

-1

Sample Output
2

3

3

5
1234567891
3

3

13

179

271

1381

2423
30971

411522630413

Source: University of Waterloo Local Contest 1996.09.28

解题报告：

首先一看没太看懂，再看才发现，原来就是因式分解。代码如下：

#include <stdio.h>
int main(){
long long i,n;
while(scanf("%lld",&n)==1&&n>=0){
for(i=2;n>1;){
if(n%i==0){
printf("%lld\n",i);
n/=i;
}
else{
i++;
if(i*i>n){
printf("%lld\n",n);
break;
}
}
}
printf("\n");
}
return 0;
}