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pushpitkc
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If p is an integer and 3^p is a factor of 300!, what is the maximum 21 Jan 2018, 12:33
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

61% (01:30) correct 39% (01:46) wrong based on 472 sessions

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If p is an integer and 3^p is a factor of 300!, what is the maximum possible value of p?

A.100
B.101
C.133
D.147
E.148

Source: Experts Global
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Official Answer
E
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stonecold
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If p is an integer and 3^p is a factor of 300!, what is the maximum 21 Jan 2018, 12:49
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Number of primes p in n! -> Remainder addition of [n/p + n/p^2 + n/p^3...]


Number of threes in 300! ->
=>300/3 + 300/9 + 300/27 + 300/81 + 300/243
=> 100 + 33 + 11 + 3 + 1
=> 148

Smash that E.
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If p is an integer and 3^p is a factor of 300!, what is the maximum 21 Jan 2018, 12:59
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stonecold
Number of primes p in n! -> Remainder addition of [n/p + n/p^2 + n/p^3...]


Number of threes in 300! ->
=>300/3 + 300/9 + 300/27 + 300/81 + 300/243
=> 100 + 33 + 11 + 3 + 1
=> 148

Smash that E.
Show more

Hi stonecold :-) i think you smashed correctly :)

can you please advice (if you know any) some article about how to solve such kind of questions "3^p is a factor of 300!"

i had no idea how to approach it, :-)

thanks! :-)
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If p is an integer and 3^p is a factor of 300!, what is the maximum 21 Jan 2018, 17:32
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Can this method be used as 2^n aswell?

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If p is an integer and 3^p is a factor of 300!, what is the maximum 21 Jan 2018, 21:42
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Hey ra5867 & dave13

Please find below the link to the thread on factorials
https://gmatclub.com/forum/everything-a ... 85592.html

Under this, you will find the detailed explanation under
Finding the powers of a prime number p, in the n!

Hope this helps!
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If p is an integer and 3^p is a factor of 300!, what is the maximum 21 Jan 2018, 23:29
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pushpitkc
If p is an integer and 3^p is a factor of 300!, what is the maximum possible value of p?

A.100
B.101
C.133
D.147
E.148

Source: Experts Global
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\(\frac{300}{3} = 100\)
\(\frac{100}{3} = 33\)
\(\frac{33}{3} = 11\)
\(\frac{11}{3} = 3\)
\(\frac{3}{3} = 1\)

So, the maximum possible value of p will be 100 + 33 + 11 + 3 + 1 = 148 , answer must be (E)
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Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
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If p is an integer and 3^p is a factor of 300!, what is the maximum 21 Jan 2018, 23:31
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ra5867
Can this method be used as 2^n aswell?

Sent from my SM-N910C using GMAT Club Forum mobile app
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Everything about Factorials on the GMAT
Power of a Number in a Factorial Problems
Trailing Zeros Problems

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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If p is an integer and 3^p is a factor of 300!, what is the maximum 22 Jan 2018, 00:02
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dave13
stonecold
Number of primes p in n! -> Remainder addition of [n/p + n/p^2 + n/p^3...]


Number of threes in 300! ->
=>300/3 + 300/9 + 300/27 + 300/81 + 300/243
=> 100 + 33 + 11 + 3 + 1
=> 148

Smash that E.

Hi stonecold :-) i think you smashed correctly :)

can you please advice (if you know any) some article about how to solve such kind of questions "3^p is a factor of 300!"

i had no idea how to approach it, :-)

thanks! :-)
Show more

Check this post for a detailed discussion:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... actorials/
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If p is an integer and 3^p is a factor of 300!, what is the maximum 28 Jan 2018, 11:20
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The official answer is E!

Official Explanation by Experts Global

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If p is an integer and 3^p is a factor of 300!, what is the maximum 25 Dec 2025, 16:43
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