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

For 3K to be a factor of p both 3 and k should be factors of p.

As p is the product of the integers from 1 to 30, inclusive,3 is one of the factors.

A quick glance to find out which is the highest answer choice, that falls within 1 to 30 (inclusive), gives us ---> E. 18

So the Ans is E.

The question should be: If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18

answer is 14

in 30! we have 3, 14 times
There are 10 multiples of 3 , so 10 + 1(for 9) + 1 (for 18) 2(for 27) = 14


So the highest value of k=14

...Cant do much abt question changes after the exam