common measure vs common factor

common measure and common factor both are nouns.

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

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

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

Other synonyms of common measure include common divisor.

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