# short cut for this question.

If p is the product of the integers from 1 to 30, inclusive, what is the greatest

integer k for which 3k is a factor of p?

(A) 10

(B) 12

(C) 14

(D) 16

(E) 18

Question is asking, maximum value of k for which 3^k is factor of p(=30!).

Strategy: go on dividing 30 by 3, since the maximum base value of k is 3, until division is not possible. Lastly, add all the quotients. That is the maximum value of k.

Solution: 30/3 –> 10

10/3 –> 3

3/3 –> 1

Adding, 10+3+1=14 Ans.

I hope this is the right answer choice and helped you.

Thanks,

Aditya Aryan