+738 What is the greatest prime number that evenly divides \(20!-19!-18!-17!\)?
any help is appreciated!
:)
+23246 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.
+738 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?
