SOLUTION: What is the greatest positive integer n such that 2^n is a factor of 12^10? I don't even know where to start!!!

Algebra ->  Exponents -> SOLUTION: What is the greatest positive integer n such that 2^n is a factor of 12^10? I don't even know where to start!!!      Log On


   

Question 147490: What is the greatest positive integer n such that 2^n is a factor of 12^10?
I don't even know where to start!!!
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
I am thinking this:
We are being asked to find the largest value of n such that 12%5E10%2F2%5En is an integer
12%5E10%2F2%5En =
%284%2A3%29%5E10%2F2%5En
%284%5E10%2A3%5E10%29%2F2%5En
%28%282%5E2%29%5E10%2A3%5E10%29%2F2%5En
%282%5E20%2A3%5E10%29%2F2%5En
2 will never factor into 3, since both are prime. So the largest number for n is the largest one that still results in %282%5E20%29%2F2%5En being an integer. What is the smallest number that still is a positive integer? well, that's 1. So what value of n results in %282%5E20%29%2F2%5En is 1? n = 20