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

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If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 11:33
1
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (01:19) correct 46% (01:53) wrong based on 79 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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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 11:49
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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 11:59
stonecold wrote:
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! :-)
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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 16:32
Can this method be used as 2^n aswell?

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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 20:42
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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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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 22:29
pushpitkc wrote:
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

\(\frac{300}{3} = 100\)
\(\frac{100}{3} = 33\)
\(\frac{33}{3} = 11\)
\(\frac{11}{3} = 3\)
\(\frac{3}{3} = 1\)

So, the maximum possible value of p will be 100 + 33 + 11 + 3 + 1 = 148 , answer must be (E)

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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 22:31
ra5867 wrote:
Can this method be used as 2^n aswell?

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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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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 21 Jan 2018, 23:02
dave13 wrote:
stonecold wrote:
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! :-)


Check this post for a detailed discussion:
https://www.veritasprep.com/blog/2011/0 ... actorials/
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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum  [#permalink]

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New post 28 Jan 2018, 10:20
The official answer is E!

Official Explanation by Experts Global


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Re: If p is an integer and 3^p is a factor of 300!, what is the maximum &nbs [#permalink] 28 Jan 2018, 10:20
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