When stating a number of things or describing their qualities, no есть is used, as its purpose is declaring existence, not giving details.
Still, with an emphasis on три, such a sentence is acceptable. For example, it would be OK in an article when you then tell which factories are these or where they are ("Напомним, у бизнесмена три завода: ... ")
While "plant" can be a synonym for "factory" in English, it usually needs to be modified in order to make sense. So, "he owns three paper plants" would be fine, or even "he owns three plants" if we already know what kind of plants they are. "Factory" works better as a generic term without additional context.