Last non-zero digits of a very large factorial

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How can one calculate the last few non-zero digits of a factorial of a large number?

By large, i mean like n=10^100 or something
(EDIT : 10^100 is the magnitude of 'n' in n! )
By few, i mean till 7-8...

I tried googling it and found this -

Last non-zero digit of a factorial

I tried to expand this to last 2 non-zero digits or more, but failed...

I found other websites on google that showed how to calculate last x number of digits but it wasn't clear and i wasn't able to understand it...

Can anyone help me with this?

Also, am not able to get this, the last two non-zero digits of 99! are 64, so i figured that the last two non-zero digits of (199! / 99!) should also be 64, but they turn out to be 24, i know i am making an extremely big logical mistake in this one, am just not able to put my finger on it!

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