common factor vs common divisor

common factor and common divisor both are nouns.

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

As nouns, common factor and common divisor are synonyms defined as:

common factor and common divisor: an integer that divides two (or more) other integers evenly

Other synonyms of common factor include common measure.

common factor (noun)	common divisor (noun)
an integer that divides two (or more) other integers evenly	an integer that divides two (or more) other integers evenly