Factories are required for producing your own weapons, tanks, aircraft as well as to increase growth and produce manufactured goods. You can currently send your self-produced weapons to other users at the cost reputation, or sell them on the open market for a similar reputation hit. The price for a factory depends on how many factories you already own. The function y=50x+25 describes the price for the factory (in oil and 2 rm) where x stands for how many factories you already own. Meaning that if you buy your first factory it will cost 25 oil and 50 RM and if you buy your second one it will cost 75 oil and 150RM and so forth. This is decreased for countries in the Asia region.
Alternatively, you have a chance to get an event where a Nike Factory can be built with your permission.
Factories also increase growth by 1M per turn per factory and produce Manufactured Goods at 1 ton per turn per factory as long as they are supplied with 1 RM and 1 oil per turn per factory. However building the factory will decrease your Quality of Life by one or two levels.
To manufacture your own AK Presidente rifles you need to have 2 factories. Every self-produced AK rifle increases Equipment and costs 5MG. You lose this option after you reach Almost Modern Tech.
To manufacture your own aircraft you need 3 factories (down from 5).
When you are at Vietnam Tech you get the option to produce Istan Main Battle Tanks which costs 13 MG and 5 Oil.
Weapons and Tanks are purchased in the military policies tab.
When your technology reaches advanced (2000+ weapons), you'll need 8 factories to make Despot Main Battle Tanks which cost 18 MG and 13 Oil.