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The phrase "a principal factor" is correct and usable in written English.
It can be used when discussing the main or most important element contributing to a situation or outcome.
Example: "The study revealed that a principal factor in the success of the project was effective communication among team members."
Alternatives: "a key element" or "a major contributor".
Exact(57)
The talks also underscore a principal factor behind the mergers, the high cost of technology.
The Arabic language was a principal factor in uniting peoples who differed widely in ethnicity, language, and culture.
These local associations of worshipers appear to have been a principal factor in the spread of the new cults.
The collapse of a speculative bubble in real estate in the late 1980's has been a principal factor in the country's economic troubles since then.
A principal factor in the cover-up, the government study found, was a Vatican letter in 1997 warning Irish church leaders against full cooperation with law enforcement authorities.
The concern about deflation was a principal factor behind the decision by the Federal Reserve in August to carry out its bond purchasing program.
That fear of deflation was a principal factor behind the decision in August to set the stage for the bond purchases.
"We're certain the disfavor and the antagonism in the black community toward the police is a principal factor in why so few black men want to become police officers," he said.
Tara Bahrampour (NYT) BUFFALO: INDIAN LAND CLAIM -- The question of who owned Grand Island and other islands in the Niagara River 200 years ago has emerged as a principal factor in the Seneca Nation of Indians' current claims to ownership.
Similar(2)
In line with the conceptual model, items representing the core domains (physical, social and emotional) were subject to a principal component factor analysis, with three factors extracted.
The factor structure of the auditory hallucinations was explored using a principal component factor analysis with a single varimax rotation.
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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