I'm having troubles applying this theorem. IT states Given any integer n > 1, there exist a postive integer k, distinct prime numbers p1,p2,...,pk, and positve integers e1,e2,....ek such that(adsbygoogle = window.adsbygoogle || []).push({});

n = p1^(e1)p2^(e2)p3^(e3)...pk^(ek), and any other expression of n as a product of prime numbers is identical to this except, perhaps, for the order in which the factors are written. The book gives 1 example,

1176 and the answer in the back is, (2^3)(3)(7)^2. I have no idea how they figured this out. Is there a trick or can someone explain that theorem better?

Thanks!

I am trying to figure out 3675, also i'm not allowed to use a calculator.

Also i'm trying to figure out how many 0's are at the end of (45^8)(88^5), the answer is 8 zeros because i used the calculator. But he said u can do it without, the book says, hint: 10 = (2)(5). 45 = (9)(5) = (3)(3)(5); 88 = (22)(4) = (22)(2)(2) but i'm not seeing how this is helping me much

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# Homework Help: Confused on how to apply THe Unique factorzation Theorem

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