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

 May 1, 2022
 #1
avatar+2440 
+1

It is 13. Because a prime number has 0 factors, it can't be any bigger. 

 May 1, 2022
 #2
avatar+9459 
+1

We factorize it first.

 

\(11! + 12! + 13! = 11! (1 + 12 + 12 \times 13) = 13^2 \times 11!\)

All prime factors of \(11!\) are smaller than or equal to 11 since \(11! = 11 \times 10 \times 9 \times \cdots \times 2\times 1\).

 

The largest prime factor is 13.

 May 2, 2022

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