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The phrase "a third factor" is correct and usable in written English.
It can be used when discussing an additional element or variable that influences a situation or outcome, often in contexts like research, analysis, or decision-making.
Example: "In our study, we identified a third factor that significantly impacted the results, which had not been considered previously."
Alternatives: "an additional factor" or "a supplementary factor".
Exact(60)
A third factor is style.
An opposition leader, Yossi Sarid, added a third factor.
A third factor is simply the passage of time.
A third factor is the flow of information.
And there is a third factor - and an important one.
Beyond instinct and availability, there's a third factor: marketing.
A third factor is fear of Italy itself.
A third factor results from the gains of the feminist movement.
A third factor may be obvious, but it is not widely understood.
A third factor is that Moldova is yet another country facing economic crisis.
Mr. Schuman, however, writes that economists have overlooked a third factor in the Asian economic miracle.
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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