What is the last non - zero digit in (20!)!? (That is, factorial of 20 factorial).

(In reply to simple solution by Tristan)

"making x!'s last nonzero digit repeat every 40"

The last non-zero digit does not repeat every 40.

Here are the last digits of the factorials of the first few multiples of 40:

 40      2


 80      8


 120     6


 160     6


 200     2


 240     6


 280     4


 320     4


 360     6


 400     8


 440     2


 480     6


 520     6


 560     4


 600     6


 640     8


 680     4


 720     6


 760     4


 800     6


 840     6


 880     6


 920     8


 960     6


 1000    2


 1040    4


 1080    6


 1120    2


 1160    8


 1200    6


 1240    8


 1280    6


 1320    6


 1360    4


 1400    4


 1440    6


 1480    8


 1520    4


 1560    6


 1600    4

--------
For the first couple,

40! = 815915283247897734345611269596115894272000000000
80! = 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000

Posted by Charlie on 2003-12-22 08:43:51