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

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If m = 3^n, what is the greatest value of n for which m is a  [#permalink]

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New post Updated on: 23 Jul 2013, 08:00
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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

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Originally posted by hb on 23 Jul 2013, 07:52.
Last edited by Bunuel on 23 Jul 2013, 08:00, edited 1 time in total.
Edited the question.
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Re: If m = 3^n, what is the greatest value of n for which m is a  [#permalink]

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New post 23 Jul 2013, 08:17
4
4
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

We should find the highest power of 3 in 25!: \(\frac{25}{3}+\frac{25}{3^2}=8+2=10\) (take only the quotient into account).. So the highest power of 3 in 25! is 10.

Answer: B.

Theory on this: everything-about-factorials-on-the-gmat-85592.html

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Hope it helps.
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Re: If m = 3^n, what is the greatest value of n for which m is a  [#permalink]

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New post 20 Apr 2014, 17:57
If m=3n, what is the greatest value of n for which m is a factor of 25!?

Solution-
Consider multiples of 25!=> 3,6,9,12,15,18,21,24
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
18=3x3x2->2
21=3x7->1
24=3x8->1

---- count 3's =10 so answer is 10

=> 25!/3x3x3x3x3x3x3x3x3x3
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Re: If m = 3^n, what is the greatest value of n for which m is a  [#permalink]

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New post 27 Jun 2017, 16:50
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"
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Re: If m = 3^n, what is the greatest value of n for which m is a  [#permalink]

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New post 03 Apr 2018, 08:23
The answer must be B, i.e. 3 will have a total power of 10 in 25!.
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Re: If m = 3^n, what is the greatest value of n for which m is a &nbs [#permalink] 03 Apr 2018, 08:23
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