Wikipedia, "Factor (Unix)" with an interesting take:
factor first appeared on 5th edition Research Unix in 1974, as a "user maintained" utility (section 6 of the manual). In the 7th edition in 1979, it was moved into the main "commands" section of the manual (section 1). From there, the factor utility was copied to all other variants of Unix, including commercial Unixes and BSD. In some variants of Unix, it is classified as a "game" more than a serious utility, and therefore documented in section 6.
So it would seem that some user(s) liked to play around with prime factors and wrote factor - and once it existed, there probably was no good reason not to include it as a command in subsequent Unix versions. So the "practical uses" of factor may depend on what you consider practical - if you are into prime number theory, it is probably a great tool/game/whatever.