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The phrase "a single factory or" is correct and usable in written English.
It can be used when discussing options or alternatives, particularly in a context where you are comparing or contrasting different entities or choices.
Example: "We can either invest in a single factory or consider multiple smaller facilities to diversify our production capabilities."
Alternatives: "one factory or" or "a solitary factory or".
Exact(3)
A Russian government study counted 467 cities and 332 smaller towns that depend on a single factory or mine.
The group is focusing on building a treatment system that could be used in developing countries to clean relatively small amounts of wastewater — say, from a single factory or a group of homes, she said.
During the 1990s union membership and power began to decline, and enterprise bargaining (i.e., within a single factory or company) and individual contracts increasingly took the place of the old centralized wage-fixing system, although the AFPC still sets minimum rates.
Similar(54)
In other cases, workers from different provinces with different cultural traditions coming together in a single factory have clashed over social issues or perceived slights.
One or many behaviour groups can be defined within a single factory.
Yet he had never bothered to visit a single factory.
"But not a single — not a single — factory worker went out there," he said.
Today, a problem at a single factory can swiftly lead to an outbreak that extends nationwide.
In Bangladesh, several unions might represent employees in a single factory.
Planar is consolidating production of its electroluminescent display panels into a single factory in Espoo, Finland.
He described how unrest could occur in industrial cities that depend on a single factory, if the factory closes.
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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