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The phrase "a third important factor" is correct and usable in written English.
You can use it when discussing multiple factors or elements in a context where you are identifying the significance of the third one among them.
Example: "In addition to cost and quality, a third important factor to consider is the timeline for project completion."
Alternatives: "a third key element" or "a third significant aspect".
Exact(8)
A third important factor in today's show dancing is the revivals.
A third important factor affecting Tibetan herders, whether recognized by them or not, is climate change.
Winton et al. (2016) argue that a third important factor to consider when designing training is the way in which it will be delivered, especially in light of the needs of the individual receiving it and the content of what is being learned.
While our selective memory owes debts to the allure of the Olympics and a tendency to privilege familiar political struggles, we must also acknowledge a third important factor.
A third important factor which could influence the association within these studies is the population under scrutiny.
A third important factor relevant to any discussion of widening the use of statins is the viewpoint of the patient, and unanswered questions abound.
Similar(52)
A second important factor is the environmental matrix.
A second important factor is the specific formula used to translate votes into seats.
Further, air entrainment as a second important factor governing mixture preparation is discussed in combination with air-distributed and fuel-distributed mixture preparation, combustion chamber design, in-cylinder flow (swirl, turbulence, etc).
A second important factor determining the patients outcome is the pressure of the gun ejection.
A fourth important factor is the site of injection, especially concerning large volumes.
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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