# how do I find the prime power decomposition of this number?

I have sat for about 8 hours doing trial and error and I have tried all combinations of different prime numbers but I am totally stuck..

I know that prime power decomposition is suppose to be prime number to the power of integers and their product gives you the original number... but I am asked to break this number down into its prime power decomposition.

412023436986659543855531365332575948179811699844327982845455626433876445565248426198098870423161841879261420247188869492560931776375033421130982397485150944909106910269861031862704114880866970564902903653658867433731720813104105190864254793282601391257624033946373269391

i have tried trial division which miserably failed after 1000, and now I am trying to divide the number into the largest prime number I can find and take the quotient I get and try to factor that into the largest prime number it can fit and so on until i have it all factored....is this even possible?

There is some browser problem I am having where comment button on stack isnt working.

This is one of the 8 assignment questions I have been assigned. I have finished all others and this I cant do from past 8 hours...

Should I write down all the prime numbers that are smaller than this number /2? and then try to break this up into those?

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Are you serious?! –  Salech Alhasov Mar 4 '12 at 4:20
What does "sqrt divisions" mean? If this is an assignment, what techniques have you been discussing? If it is not an assignment, then why are you trying to factor this? –  Arturo Magidin Mar 4 '12 at 4:23
Which begs the question, yet again: what factoring techniques have you discussed in your class? Obviously you are supposed to be trying to use them. P.S. If you were really going to do trial division, you only have to go up to $\sqrt{n}$, not up to $n/2$. –  Arturo Magidin Mar 4 '12 at 4:44

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