Factoring Large Numbers
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Factoring Large Numbers
One of the central ideas 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. You may assume that there will be at most one factor more than 1000000.
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 with 4 leading spaces preceding a left justified number, and followed by a single blank line.
Sample Input
901234567891#include<iostream>#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;long long n, h = 0;int arr[1000010];int prime(int x){int i; for (i = 2; i * i <= x; i ++){if (x / i == 0){return 0;}}return 1;}void isprime(){int i;for (i = 2; i <= 1000010; i ++){if (prime(i)){arr[h ++] = i;}}}int main(){int j, arr1[10000], k;isprime();while (scanf("%lld", &n) && n >= 0){k = 0;for (j = 0; j < h; j ++){while (n % arr[j] == 0){arr1[k ++] = arr[j];n /= arr[j];}if (n <= 1){break;}}for (j = 0; j < k; j ++){printf(" %d\n", arr1[j]);}if (n != 1){printf(" %lld\n", n);}printf("\n");}return 0;}
1899132545313912745267386521023-1
Sample Output
2 3 3 5 1234567891 3 3 13 179 271 1381 2423 30971 411522630413
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