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Re: What is the greatest prime factor of 12!11! + 11!10!
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15 Dec 2014, 09:16

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uday1409 wrote:

What is the greatest prime factor of 12!11! + 11!10!?

(A) 7 (B) 11 (C) 13 (D) 17 (E) 19

12! = 12.11.10! 12!11!+11!10! = 12.11.10!.11! +11!.10! taking 11!.10! common we have 11!.10!(12.11+1) 11!.10!(133) 11!.10!(19.7) as can be see the greatest prime factor is 19 hence answer is E

Re: What is the greatest prime factor of 12!11! + 11!10!
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16 Dec 2016, 12:45

12!11!+11!10! = 11!(12!+10!) Since 11! has only 11 as the largest prime number, we exclude it from further processing. 12!+10! = 10! (11*12+1) = 10! (133) 133 = 7 * 19 19 - is prime number that is to be the highest one, answer E is correct.

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16 Dec 2016, 13:07

uday1409 wrote:

What is the greatest prime factor of 12!11! + 11!10!?

(A) 7 (B) 11 (C) 13 (D) 17 (E) 19

let 10! = x ( greatest prime is 7)

12! = 12*11*x = 132x 11! = 11x

(132x)*(11x)+(11x)*x = (11x)*(133x)

133 = 19*7 thus (11x)*(133x) = (19*11*7)x^2 and since the greatest prime in x = 7 still the greatest prime in x^2 is 7 and thus greatest prime is 19......E