Let’s start with your first assumption. Why must a factory have individual owners? Why not instead have it owned by the workers who are the ones actually producing?
Also, don’t conflate private and personal property. If you are indeed talking about private property, it is very unlikely you have any to begin with. The vast majority of private property is owned by a few billionaires.
Lastly, people do not need money to incentivise work. Boredom, creativity and the desire to help and or contribute to society does that well enough. Given a stable level of comfort, people will seek work that matters to them.