SOLUTION: What is the greatest power of 3 that divides into 578!, with no remainder.

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Question 1149796: What is the greatest power of 3 that divides into 578!, with no remainder.
Answer by ikleyn(52848) About Me  (Show Source):
You can put this solution on YOUR website!
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578%2F3 = 192.66  gives you the factor  3%5E192.


578%2F3%5E2 = 64.22  gives you additional factor of  3%5E64.


578%2F3%5E3 = 21.41  gives you additional factor of  3%5E21.


578%2F3%5E4 = 7.43  gives you additional factor of  3%5E7.


578%2F3%5E5 = 2.37  gives you additional factor of  3%5E2.


578%2F3%5E6 = 0.79  will NOT give you additional factor of 3.


So, the maximal degree of 3 is   192 + 64 + 21 + 7 + 2 = 286.    ANSWER