Division

A lot of questions seem easy after you see someone else do it.  I quite like questons like this because they make you think about how numbers interact :)

(1! + 2! + 3! + 4! + ... + 100!)  / 36  ; What is the remainder of this division?

I found 9 via the calculator, but how can i solve this problem without being too harsh on it... :( I can't believe i just tried to calculate it on the calculator but if there's a formula or something it will really help me. :) 

Mmm,     36=1*2*3*  6

so from 6! up to 100! there will be no remainders so I am only going to look at

(1!+2!+3!+4!+5!)/36 = (1+2+6+24+120 )/36  =  153/36  =  (144+9)/36

The remainder will be 9.

Can you understand my logic?