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What is the greatest prime factor of (13!12!) + (13!14!)?

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What is the greatest prime factor of (13!12!) + (13!14!)? [#permalink]

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New post 21 Jan 2015, 01:30
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A
B
C
D
E

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  55% (hard)

Question Stats:

47% (00:55) correct 53% (01:07) wrong based on 148 sessions

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Kudos [?]: 135739 [0], given: 12707

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Re: What is the greatest prime factor of (13!12!) + (13!14!)? [#permalink]

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New post 21 Jan 2015, 06:23
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D 61.... take out common 13!12!(1+14*13)=13!12!183...in 183 ,61 is the largest prime number
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: What is the greatest prime factor of (13!12!) + (13!14!)? [#permalink]

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New post 22 Jan 2015, 02:17
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Answer = D = 61

13!12! + 13!14!

= 13!12! + 13! * 14 * 13 * 12!

= 13!12!(1 + 169+13)

= 13! 12! * 61 * 3

GCD = 61
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Re: What is the greatest prime factor of (13!12!) + (13!14!)? [#permalink]

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New post 27 Jan 2015, 07:16
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Or with a few more steps:

13!12! + 13!14!
12!12!13 + 13!13!14
12!12!13 + 12!12!*13*13*14
12!12!13 (1+13*14)
12!12!13*183
12!12!13*3*61

So, ANS D

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Re: What is the greatest prime factor of (13!12!) + (13!14!)? [#permalink]

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New post 04 May 2016, 13:09
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(13!12!) + (13!14!)
13!12! x ( 1+ 14 x 13)
13!12! x 183
13!12! x 3 x 61

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Re: What is the greatest prime factor of (13!12!) + (13!14!)? [#permalink]

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New post 22 Nov 2016, 00:54
Great Question
Here is what i did
N=12!*13![1+14*13]
N=12!*13!*183
N=12!*13!*3*61
61=> Prime Number
Hence greatest Prime is 61

Hence D
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Re: What is the greatest prime factor of (13!12!) + (13!14!)? [#permalink]

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New post 27 Nov 2017, 14:35
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Re: What is the greatest prime factor of (13!12!) + (13!14!)?   [#permalink] 27 Nov 2017, 14:35
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