common factor vs divisor

common factor and divisor both are nouns.

Word	Noun	Adjective	Verb	Adverb
common factor	Yes	No	No	No
divisor	Yes	No	No	No

As nouns, divisor is a hypernym of common factor; that is, divisor is a word with a broader meaning than common factor:

common factor: an integer that divides two (or more) other integers evenly
divisor: one of two or more integers that can be exactly divided into another integer

Other hypernyms of common factor include factor.

common factor (noun)	divisor (noun)
an integer that divides two (or more) other integers evenly	the number by which a dividend is divided
	one of two or more integers that can be exactly divided into another integer