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Find the largest prime divisor of 11! + 12! + 13!.

 Dec 15, 2021
 #1
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11!  +  12!  +13! ==6,745,939,200

 

6745939200 = 2^8 * 3^4 * 5^2 * 7 * 11 * 13^2

 

The largest prime divisor ==13

 Dec 15, 2021
 #2
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11! + 12! + 13!

 

=11!(1+12+12*13)

=11!*169

=11! * 13 *13

 

so yes the largest prime is 13

 Dec 15, 2021

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