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What is the maximum value of m such that 7m divides into 14!

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Intern
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What is the maximum value of m such that 7m divides into 14! [#permalink] New post 30 May 2018, 01:45
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Question Stats:

83% (00:15) correct 16% (00:00) wrong based on 6 sessions
What is the maximum value of m such that 7^m divides into 14! evenly?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5
[Reveal] Spoiler: OA
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Manager
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Joined: 06 Jun 2018
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Re: What is the maximum value of m such that 7m divides into 14! [#permalink] New post 06 Jun 2018, 11:18
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shahul wrote:
What is the maximum value of m such that 7^m divides into 14! evenly?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5


Note: 7^m divides 14!. Thus we understand that 7^m is basically a factor of 14!.

The you can find out the maximum number of m as a power of 7 as follows:

n/x^1 + n/x^2+......so on...

14/7
=2

m must be 2 as a power of 7.

Hope it clears.


Alternate way:

14!=1*2*3*34*5*6*7*8*9*10*11*12*13*13*14
=1*2*3*4*5*6*7*8*9*10*11*12*13*7*2
= \(7^2\)*1*\(2^2\)*3*4*5*6*8*9*10*11*12*13

So in total we have 2..........7
Re: What is the maximum value of m such that 7m divides into 14!   [#permalink] 06 Jun 2018, 11:18
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What is the maximum value of m such that 7m divides into 14!

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