How can I do this please..

[MagicJamie]

I'll start off by saying "Hi", since this is my first post on this forum.

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First here's some examples:

37789 x 3256 = 123040984
4326 x 456765347 = 1975966891122
5327 x 467 = 2487709

Ok, now here's the problem I am facing... I would like to do the reverse of what I have shown above. I start off with a large number and I would like to find 2 INTEGER numbers, which when multiplied together gives you the results of the starting number. (ie. 210950 = 8438 x 25)

Is there a way I can do this? Btw, please explain in novice terms since I am new to learning math.

Or if anyone is kind enough to write a simple Windows, DOS, or Flash based program which would do that for me, that would be even better. That way I could type in a large number and then press enter and then it lists many different combinations to choose from. This would save me ALOT of time in the long run, since I need to do this with hundreds, maybe even thousands of numbers.

There is a BIG reason why I need to do this, but I wont go into the reasons why I need it since it would take too long to explain, and I would probably bore you all to death with my story, and my fingers would hurt badly from all the typing. hehe

[Saul]

This should be useful:
http://www.cryptographic.co.uk/factorise.html
It's a java applet. Instructions are on the page.

[MagicJamie]

[Saul]

one way to get around that, if you have a calculator, is to just put all those numbers into two sets and multiply each set together. So for 543543 you could get (3.7.11) x (13.181) = 231 * 2353 = 543543.

[tokenadult]

Factoring an arbitrarily selected integer is a difficult problem that increases in difficulty RAPIDLY as the integer to be factored grows larger. Most computer algebra systems (e.g., Mathematica) have integer-factoring capabilities that do well up to a fairly large number of digits. BUT most public-key encryption schemes, such as the secure online connections used in online commerce, count on factoring large integers being so difficult that it is practically impossible in reasonable amounts of time. If someone finds a handy-dandy way to factor an integer of any moderate size rapidly, he will cause billions of dollars of changes in the world economy.

[SnowStorm]

If you want a good list of factors.
1) Find the prime factorization of the number. (ie the prime factorization of 543543 is )
2) Any combination of these numbers multiplied into 2 numbers will give you what you want, for example:



There are a lot more, but this gives you the general idea.

[qweretyq]

[probability1.01]

Well public key-private key uses some pretty large primes... a couple hundred digits long I think