You just have to be friendly with the factory to do this you can go into the factory shop then click local shop and bribe them or look for a civ and do a mission for them once you are friendly it will take a little while then the factoy will be yours

I have a friendly reputation with the factory, even did few missions because I thought they are "friendly, but not so friendly". The only factory I can use is the one on the center of the map, others don't work.

Try setting up a gard post there

Tried, still the same, only the local shop available. It says on the hud, that the factory is guarded and operative. As I said, I can buy everything from the factory near Agios Dionysios, but from others: I can't.

Have you tried reloading your save?

Yeah, many times. All factories work as they should on other maps, but on Altis, they don't.

Not sure if this is still relevant or still a problem for anybody but I figured I should post. I once switched my language to Polish and that actually seemed to be the problem. So if anybody is having this problem and has switched their language to anything other than English, try switching to English and see if it works. I think it has something to do with the factories getting renamed on the Altis map. Example: When I switched to Polish, the name changed from "factory" to "fabryka." Hope this helps.