Where can I find the article.cls class file of texlive-2016 on my pc?

The easiest way to find any file in the TeX Distribution (if you know its name) is to use the kpsewhich program.

From the command line type:

kpsewhich article.cls

and it should return:

/usr/local/texlive/2016/texmf-dist/tex/latex/base/article.cls

on a TeX Live system.

Depending on your OS, you may be able to open the file directly. On a Mac, e.g. I can type

open `kpsewhich article.cls` 

and the file will open in my normal TeX editor. (The back ticks pass the output of the command within the back ticks to the open command.) The equivalent Linux command is xdg-open I believe. I have no idea if an equivalent command exists in Windows.