Factious is an adjective describing something or someone has having to do with factions, or separate groups within a larger body, usually separated by a belief or proclivity. It has derivatives of factiously and factiousness, though these are rarely used.
It is pronounced \ˈfak-shəs\ (fact shish).
Facetious, on the other hand, is a word to describe something or someone as intentionally funny, though usually failing to attain humor or inappropriate. It also has two derivatives of facetiously and facetiousness.
It is pronounced \fə-ˈsē-shəs\ (fah see shish).