SOLUTION: The question is: What is the greatest positive integer n such that 2^n is a factor of 12^10? I guessed and got the answer correct: 20. But I don't know how to work this proble

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Question 106924: The question is:
What is the greatest positive integer n such that 2^n is a factor of 12^10? I guessed and got the answer correct: 20. But I don't know how to work this problem.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
12^10=(2^10)(2^10)(3^10)=(2^20)(3^10)

3^10 is odd and has no even factors (no 2's) ... so 2^20 is largest power of 2 in 12^10