KVPY #22

$Last~ non~ zero~ digit~ of~ N!~~ is the~ last~ nonzero~ digit~ of~~ 2^A*A!*B!.\\ where~~N~=~5A~+~B,~~~0\leq~B<5.\\ 400=5*80+0~~\implies~~A=80, ~~~B=0.\\ 80!=10!*\dfrac{20!}{10!}*\dfrac{30!}{20!}*\dfrac{40!}{30!}*\dfrac{50!}{40!}*\dfrac{60!}{50!}*\dfrac{70!}{60!}*\dfrac{80!}{70!}\\ Product~of~last~nonzero~digits~from~calculator~=~8*4*4*2*8*8*4*2*8=48.\\ Last~ non~ zero~ digit~ of~ 80!=\color{#3D99F6}{8}.\\ Last~ non~ zero~ digit~ of~ 2^{80}=\color{#3D99F6}{6}.\\ Last~ non~ zero~ digit~ of~ 400!=last~ non~ zero~ digit~ of~2^{80}*80!*0!=8*6*1=\Large~~\color{#D61F06}{8}.\\$

My DESMOS High Precision calculator had 102 digits and $\dfrac{80!}{70!}$ were more than 102 digits. So I had divided $\dfrac{80!}{70!}~by~10^{14}.$
Similarly when calculator answered by going to scientific mode I have used the same method to retain last digit.
I started with 10! and in steps of 10. Depending on your calculator, you may need more small steps, say of 7 or 5 or even 3.
In fact you may use bigger steps for first small values and go on decreasing step values and dividing by power of 10 to eliminate zeros..
400!/396! has 11 digit. So your last step can be of 4. lot of work!
See link below.

link text