the.com/greatest common factor

means The largest whole number that divides evenly into two or more numbers at once.

from A plain descriptive phrase rather than a borrowed root: 'greatest' plus 'common' (shared by all the numbers in question, from Latin communis) plus 'factor' (a number that divides another evenly, from Latin facere, 'to make' — a factor is one of the numbers that 'makes' the product). The term settled into this form as arithmetic textbooks standardized vocabulary for teaching fractions and divisibility, so students in different schools could call the same idea by the same name.