I thought this was straight forward.
(13!12!)+(13!14!)
13!(12!+14!)
13!12!183
61 IS the biggest prime number that divides 183. 61 is the solution.
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Prime factorization
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immaculatesahai
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gunjan1208
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I loved this question since it gives the example what a simple question can become....if not handled properly, its hell of a vertical height mapping.
Thank you Dana J
Thank you Dana J
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mourinhogmat1
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Fantastic question! Fell for 13. But realized we need to expand/factorize such questions before we conclude.
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ronnie1985
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factoring give 183*(12!)*(13!)
Factor = 61
Factor = 61
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bhanu marwaha
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13!*12!(1+14*13)
13!*12!(183)
13!*12!(3*61)
in 13!*12! you cannot have a number which will be prime and greater than 61 )
13!*12!(183)
13!*12!(3*61)
in 13!*12! you cannot have a number which will be prime and greater than 61 )
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ronnie1985
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Ganesh hatwar
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B??? Just guess taking 13 commonDanaJ wrote:Source: Veritas Prep
What is the greatest prime factor of (13!12!) + (13!14!)?
A. 11
B. 13
C. 47
D. 61
E. 71
Hehe, really liked this one! Let's see if you can nail it!
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chris558
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D) 61
(13!12!)+(13!14!)...
Factor out common factors which in this case would be 13! and 12!
13!12!(1+(13)(14))
We know that 13!12! is not prime, so now calculate what is inside the parentheses...
1+(13)(14)=182+1=183=3(61)
61 is prime. Answe ris D.
(13!12!)+(13!14!)...
Factor out common factors which in this case would be 13! and 12!
13!12!(1+(13)(14))
We know that 13!12! is not prime, so now calculate what is inside the parentheses...
1+(13)(14)=182+1=183=3(61)
61 is prime. Answe ris D.
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surmilsehgal
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what's the quickest way to determine that 61 is the greatest prime factor of 183? i understand that I can check if it's divisible by 3 and then come to 61, but how would i konw that it's the greatest prime factor? (i'm looking at this from a DS point of view where i cant just rule out choices from the answers)
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adthedaddy
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Dear djc225,
If you factorize 183, then it has only two factors -> 3 and 61.
Thats it... 61 is prime and greatest... hence it is the greatest prime factor...
Note: The other terms are 13! and 12!
We know that the greatest prime factor of 13! is 13 and for 12! its 11.
So left is only 183 which 3*61...
Thus 61 is the greatest prime factor
If you factorize 183, then it has only two factors -> 3 and 61.
Thats it... 61 is prime and greatest... hence it is the greatest prime factor...
Note: The other terms are 13! and 12!
We know that the greatest prime factor of 13! is 13 and for 12! its 11.
So left is only 183 which 3*61...
Thus 61 is the greatest prime factor
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Kshitij Sharma
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rajeshsinghgmat
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D in answer.
(13!12!) + (13!14!)
=(13)(12!)(12!) + (13)(12!)(14)(13)(12!)
=(13)(12!)(12!)(1+13*14)
=(13)(12!)(12!)(183)
=(13)(12!)(12!)(3)(61)
(13!12!) + (13!14!)
=(13)(12!)(12!) + (13)(12!)(14)(13)(12!)
=(13)(12!)(12!)(1+13*14)
=(13)(12!)(12!)(183)
=(13)(12!)(12!)(3)(61)
