hb wrote:

If m = 3^n, what is the greatest value of n for which m is a factor of 25!

(A) 8

(B) 10

(C) 12

(D) 14

(E) 16

My Question: Please provide an explanation on how to arrive at the answer.

Disclaimer: I have used the Search Box Before Posting. I used the first sentence of the question or a string of words exactly as they show up in the question below for my search. I did not receive an exact match for my question.

Source:

Veritas Prep; Book 02

Chapter: Homework

Topic: Arithmetic

Question: 106

Question: Page 252

Solution: PDF Page 29 of 32

We don't actually have to expand 25 and count all the factors of 3 within the expansion 25- realistically that'll be too inefficient on the GMAT- so instead we can do

25/3 + 25/3^2 = 8 +2 = 10 factors ... but how do we use this for say finding the factors of 4 in "25!"?

25/4 = 6 not minding the remainder just like finding the factors of 0 in a factorial

25/4^2 = 1 again not minding the remainder

6 + 1 =7

why wouldn't we do 25/4^3? because 4^3 =64 and this is too large to go into 25- if we wanted to find the number of 7'2 in 100! it would be the same pattern

100/7 = 14

100/7^2 = 2

14 + 2 = 16 factors of 7 in 100!

Thus

"B"