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"factory by" is not a grammatically correct phrase in standard written English.
It is possible that it could be used in a specific context or dialect, but in most cases, it would not be considered correct or widely used. If you are trying to describe a factory that is located near something or someone, you could use phrases like "located by" or "nearby." For example, "There is a factory located by the river" or "The nearest factory is located nearby the city center."
Exact(60)
THE IDEA FACTORY, by Jon Gertner.
"Big Wheel at the Cracker Factory" by Mickey Hess.
Inside charlie's Chocolate Factory by Lucy Mangan (penguin £20).
The company expects to open the factory by late 2003.
The Prose Factory by DJ Taylor (Chatto & Windus, £25).
The Great British Dream Factory by Dominic Sandbrook Allen Lanee).
It isn't in a downtown basement or a converted factory by the Gowanus Canal.
Before then multinationals were often built shop by shop, factory by factory.
The Hope Factory by Lavanya Sankaran is published by Tinder Press.
I'm also reading "The Shadow Factory," by James Bamford, about the N.S.A.
A new generation of gas turbines is now being produced within the factory by Siemens.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com