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factor of 12!11! + 11!10!

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by sanju09 » Mon Feb 21, 2011 12:54 am
What is the greatest prime factor of 12!11! + 11!10!?
{A) 7
(B) 11
(C) 13
(D) 17
(E) 19
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by manpsingh87 » Mon Feb 21, 2011 1:16 am
sanju09 wrote:What is the greatest prime factor of 12!11! + 11!10!?
{A) 7
(B) 11
(C) 13
(D) 17
(E) 19
12(11)!^2+11!.10!

11!(12.11!+10!) and it can be written as 11K therefore the greatest prime factor is 11.
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by sanju09 » Mon Feb 21, 2011 1:24 am
manpsingh87 wrote:
sanju09 wrote:What is the greatest prime factor of 12!11! + 11!10!?
{A) 7
(B) 11
(C) 13
(D) 17
(E) 19
12(11)!^2+11!.10!

11!(12.11!+10!) and it can be written as 11K therefore the greatest prime factor is 11.
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by BarryLi » Mon Feb 21, 2011 1:30 am
Please spot the error in my thinking in solving this problem. I know it is an error because my answer is not any of the choices listed.

12!11! + 11!10!
12(11!)11(10!) + 11!10!
12*11*(11!10!) + 11!10!
121(11!10!) + 11!10!
122(11!10!)

122 can be factored into the primes 2 and 61, making my incorrect answer 61.
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by sanju09 » Mon Feb 21, 2011 1:35 am
BarryLi wrote:Please spot the error in my thinking in solving this problem. I know it is an error because my answer is not any of the choices listed.

12!11! + 11!10!
12(11!)11(10!) + 11!10!
12*11*(11!10!) + 11!10!
121(11!10!) + 11!10!
122(11!10!)

122 can be factored into the primes 2 and 61, making my incorrect answer 61.
My take is

12! 11! + 11! 10!

= 11! 10! (12 ×11 + 1)

= 11! 10! × 133

= 11! 10! × 7 × 19

[spoiler]19[/spoiler] is the greatest prime factor.


[spoiler]E[/spoiler]
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by BarryLi » Mon Feb 21, 2011 1:38 am
I mistook 12 * 11 = 121 instead of 132. Thank you for your post.

132 + 1 = 133, which gives your answer.
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by rohu27 » Mon Feb 21, 2011 1:43 am
12*11 is 133, got ur calculation wrong.
BarryLi wrote:Please spot the error in my thinking in solving this problem. I know it is an error because my answer is not any of the choices listed.

12!11! + 11!10!
12(11!)11(10!) + 11!10!
12*11*(11!10!) + 11!10!
121(11!10!) + 11!10!
122(11!10!)

122 can be factored into the primes 2 and 61, making my incorrect answer 61.
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by sanju09 » Mon Feb 21, 2011 1:46 am
rohu27 wrote:12*11 is 133, got ur calculation wrong.
BarryLi wrote:Please spot the error in my thinking in solving this problem. I know it is an error because my answer is not any of the choices listed.

12!11! + 11!10!
12(11!)11(10!) + 11!10!
12*11*(11!10!) + 11!10!
121(11!10!) + 11!10!
122(11!10!)

122 can be factored into the primes 2 and 61, making my incorrect answer 61.
12 X11 + 1 = 132 + 1 = 133 = 7 X 19
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by manpsingh87 » Mon Feb 21, 2011 2:02 am
sanju09 wrote:
rohu27 wrote:12*11 is 133, got ur calculation wrong.
BarryLi wrote:Please spot the error in my thinking in solving this problem. I know it is an error because my answer is not any of the choices listed.

12!11! + 11!10!
12(11!)11(10!) + 11!10!
12*11*(11!10!) + 11!10!
121(11!10!) + 11!10!
122(11!10!)

122 can be factored into the primes 2 and 61, making my incorrect answer 61.
12 X11 + 1 = 132 + 1 = 133 = 7 X 19
yeah.. my bad.. !!! didn't pay proper attention, solved it in a hurry..!!!
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by Night reader » Mon Feb 21, 2011 3:04 am
sanju09 wrote:What is the greatest prime factor of 12!11! + 11!10!?
{A) 7
(B) 11
(C) 13
(D) 17
(E) 19
12!11! = 132*11!10!
11!10!(132+1) = 11!10!*133, where 133=7*19 --> 11!10!*7*19 :)

choose E
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