This question comes from the Official Guide 12th Edition:

Problem 110 in Quant. Problem Solving:

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

This OG solves this problem by listing a table of numbers between 3 and 30 and finding all the possible factors of 3 for each of the numbers. I am wondering if there is an easier way to solve this problem. There has to.....

Their approach is actually not bad --
You don't have to write down every single number, though -- since we know that only every third number is a multiple of 3, we can just write those:
3
6
9 -- this has two 3's in it
12
15
18 -- this has two 3's in it
21
24
27 -- this has three 3's in it
30

This will probably be marginally faster, as we don't waste time with numbers we know don't contain three's...

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