What kind of word is professor is it a common noun or collective noun?

The word 'professor' is a singular, common noun, not a collective noun.

A collective noun is a word used to group people or things taken together as one whole. Some collective nouns for professors are:
a patience of professors
a pomposity of professors
a procrastination of professors
an arrogance of professors
an anthology of professors
an absence of professors
a profundity of professors
a passel of professors