SOLUTION: Find the maximum power of 91 for which 3*6*9*12....*228*231 is completely divisible?

SOLUTION: Find the maximum power of 91 for which 369*12....228231 is completely divisible?

Question 612318: Find the maximum power of 91 for which 3*6*9*12....*228*231 is completely divisible?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Note that 91 = 7*13.

Intuitively there will be fewer multiples of 13 in the set {3,6,...,231}. The multiples of 13 in the set that are less than 231 are 3*13, 6*13, ..., 15*13, five multiples of 13.

You can find the multiples of 7 but there are definitely more than five of them.

Therefore the greatest power of 91 that divides 3*6*...*231 is 91^5.
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