FACT0  Integer Factorization (15 digits)
This is a problem to test the robustness of your Integer Factorization algorithm.
Given some integers, you need to factor them into product of prime numbers.
The largest integer given in the input file has 15 digits. FACT1 is a harder version of this problem (the numbers are larger).
You may need to use a general factorization algorithm since no special numbers (e.g. Fermat numbers) are considered when designing the input data.
Input
There are several numbers given, each one in a line.
The input ends with a number 0.
The number of test cases is about 10.
Output
For each number, print in a line the factorization of it. See examples below for the output format.
Example
Input: 3111989 13091989 77145199750673 0 Output: 317^1 9817^1 17^2 89^1 509^1 328439^1 234884407^1
hide comments
chandan_5362:
20200702 10:41:10
I am getting TLE for this problem even after using sieve method in PYTHON3.


adikrmishra_1:
20200617 17:24:16
just use factorization in sqrt(n) time :)


lm10_piyush:
20191121 16:37:12
I have tried sieve with prime integer factorization but it gives me WA, anyone suggests any issue, I've test my code on many test cases it works fine.. largest number is 999999999999999 (9 15times).


zarif_2002:
20191102 09:04:02
Just do basic sieve before approaching. that's it. 

drdrunkenstein:
20190823 20:42:08
Python 3 gets tle for trial division 

scolar_fuad:
20190702 14:01:17
Easy just use primefactorization of number


karan_yadav:
20180707 10:48:37
WTF!!!


zephyr_96:
20180519 09:47:49
Precal using sieve will give TLE. Normal O(root(n)) works. : 

ameyanator:
20180401 22:16:52
Well if you know how to calculate the number of divisors of a number in sqrt(N) time then this is a easy question I guess 

jayharsh:
20170815 16:06:15
you will get TLE in brute force but optimize it and your code will work 
Added by:  Jimmy 
Date:  20091008 
Time limit:  1.138s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL NODEJS PERL6 VB.NET 