common factor vs common measure

common factor and common measure both are nouns.

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

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

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

Other synonyms of common factor include common divisor.

common factor (noun)	common measure (noun)
an integer that divides two (or more) other integers evenly	the usual (iambic) meter of a ballad
	an integer that divides two (or more) other integers evenly
	a time signature indicating four beats to the bar