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avatar+732 

What is the greatest prime number that evenly divides \(20!-19!-18!-17!\)?

 

any help is appreciated!

:)

 May 29, 2020
 #1
avatar+21953 
+1

20! - 19! - 18! - 17!  =  17! · ( 20 · 19 · 18  -  19 · 18  -  17  -  1 )

                                =  17! · ( 6479 )

                                =  17! · ( 11 · 19 · 31 )

 

So, the greatest prime factor is  31.

 May 29, 2020
 #2
avatar+732 
0

thanks!

 

i just have one question though, why is it equal to 17! · ( 20 · 19 · 18  -  19 · 18  -  17  -  1 )? why is there a -19*18-17-1?

lokiisnotdead  May 29, 2020

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