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The phrase "a unique factor in" is correct and usable in written English.
It can be used when discussing a specific element or characteristic that distinguishes something within a particular context or situation.
Example: "The company's commitment to sustainability is a unique factor in its competitive advantage."
Alternatives: "a distinguishing element in" or "a notable aspect of".
Exact(3)
A unique factor in this production is the global experience of some of these artists who have had wide exposure to international arts-making.
A unique factor in the measure of investment correlation is that it could extend to risk factors beyond the portfolio.
Consequently, the probability of becoming a cluster-head is a unique factor in determining the average energy consumed in a network.
Similar(57)
When this diet was artificially replicated and fed to squabs, their growth was either very poor or they died [ 5], which suggests there is a unique factor or factors present in pigeon 'milk' that is required for squab growth and development.
Thus, factor analysis was applied to each domain separately to evaluate whether the assumption of a unique factor satisfactorily summarizing the items in each domain was supported by the data.
Also, the loadings of these items on the first factor are lower compared to those with the unique factor in the 1-factor model.
The third column of Table 5 reports the correlations (loadings) between the PTPSQ-I(15) items and the unique factor in the 1-factor model.
But there are a few unique factors in this particular equation.
And there are always unique factors in the time and place where a study was run, everything from the state of the economy to the effectiveness of the local schools, that limit how broadly the lessons can be applied.
Having him and Jennstar in the mix brought out a large gay crowd, which I think was one of the most unique factors in what we did, and why it hasn't been able to be replicated in the city since.
They said the amounts were justified because of unique factors in each case, the applicable laws, the years of investigation and the risk of litigating in court.
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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