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The phrase "a first important factor" is correct and usable in written English.
It can be used when introducing a key element or consideration in a discussion or analysis.
Example: "When evaluating the success of the project, a first important factor to consider is the budget allocation."
Alternatives: "a primary significant factor" or "an initial crucial factor".
Exact(1)
A first important factor is education which, defined as providing knowledge and skills needed to perform diabetes self-care, manage crises and make lifestyle changes[ 12, 13], was found to improve quality of disease management and treatment adherence by child and parents [ 14- 17] and to subsequently improve the child's glycemic control [ 16, 18].
Similar(59)
A third important factor in today's show dancing is the revivals.
A second important factor is the specific formula used to translate votes into seats.
A second important factor is the environmental matrix.
A second important factor determining the patients outcome is the pressure of the gun ejection.
A third important factor affecting Tibetan herders, whether recognized by them or not, is climate change.
A fourth important factor is the site of injection, especially concerning large volumes.
A second important factor is product; it means the design, volume, and quality of product which is having an impact of 22.56 % on performance.
A second important factor in the development of his philosophical approach to understanding religion was his long-standing interest in the variety of human cultures and the dynamics of human social interaction.
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, found in Islamic commentators, was the introduction of a distinction between first and second intentions, and the understanding that the first are studied in metaphysics and other sciences that deal with the extra-mental world, whereas the second are studied in logic (Pini 2003).
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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