Need help to reverse engineer a problem...........................

[jayearl]

I hoping that someone may help me find a formula for this problem...

Starting with a specific, large-sum number (ex. 5,408,286,291),

find 4, three or four digit numbers that, when multiplied, will arrive at this large-sum number. It could
be 3 larger numbers or 4 smaller numbers. It doesn't matter really just as long as we arrive at the
final sum.

Since I'm not a math student, I'm hoping to find a formula that can accomplish this. I guess
this is basically doing multiplication backwards. I know it's probably a strange request but I figured
that someone on this forum would know now.

Thank you
Jayearl

 

[MarkFL]

Hello, and welcome to MHB, jayearl!

I've moved your thread because this forum is a better fit for the topic of the thread.

Your best bet here is to use a calculator/computer to factor the number (doing so by hand could be very tedious), for example:

W|A - Factor 5,408,286,291

On that page, we find the prime factorization:

\(\displaystyle 5,408,286,291=3^2\cdot61\cdot1049\cdot9391\)

So, if we wanted 4 factors, we could use:

\(\displaystyle 5,408,286,291=9\cdot61\cdot1049\cdot9391\)

And if we wanted 3 factors:

\(\displaystyle 5,408,286,291=549\cdot1049\cdot9391\)

 

[jayearl]

Thank you for the assistance.
But I don't believe I explained myself well.
(again, I'm not a math-guy at all so I don't know where to start)

I would like to have 3 or 4 numbers (each with 3 or 4 digits) that, when multiplied, arrive at a specific sum.
ex. 469 X 102 X 309 X 910 = _______number that I first specify______ OR
2005 X 7311 X 3017 = _______number that I first specify_______

Everyday I'll start with a new 9-digit number. Then, I'll need to work backwards? to find the factors that arrive at this new, daily sum.

Is this more clear?
Thank you again for any assitance.
Jayearl

 

[MarkFL]

Just to clear up some terminology, when you multiply several numbers together you get a product, not a sum. A sum is the result of addition. :D

There is no easy method/formula for factoring large numbers in general...so the best method is to use a calculator/computer to run known efficient algorithms for spitting out the factorization.

 

[jayearl]

I believe this is what I need to know how to do:
"so the best method is to use a calculator/computer to run known efficient algorithms for spitting out the factorization"

This is where I don't know what to do...I know even know what an algorithms is .. OR I would be willing to pay someone to figure this out for me.