Question 165477: What is the smallest positive integer n for which 324 is a factor of 6^n?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Found 2 solutions by MRperkins, Edwin McCravy:Answer by MRperkins(300) (Show Source): You can put this solution on YOUR website! Factor 324 completely:
Continue doing this until you have all of the factors of 324. It is ok to have additional factors but it is not ok to be missing any factor. notice that we are still missing a 3 in this one here we finally have two (2)'s and the four (3)'s that are in 324 and we also have two (2)'s left over.
6^4 =324(the factor of 6^4) times the two (2)'s that are left over
so 6^4=1296
Edwin is correct that (c)4 is the right answer. Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website! Edwin's solution:
What is the smallest positive integer n for which 324 is a factor of 6^n?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
Break 324 down into primes
324 = 2*2*3*3*3*3
Since 6 = 2*3, each factor of 6 contributes one factor of 2
and one factor of 3.
Since 324 has four factors of 3, we need four factor of 6 to
contribute them all.
So the answer is 4, choice (C)
Edwin