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The phrase "a factor of three" is correct and usable in written English.
It is typically used in mathematical or scientific contexts to indicate a multiplicative relationship, meaning something is three times larger or greater than something else.
Example: "The population of the city increased by a factor of three over the last decade."
Alternatives: "threefold" or "tripled".
Exact(59)
Hence the sensitivity drops by a factor of three.
Small writes through Sawmill are a factor of three faster than writes to the underlying RAID.
grows by about a factor of three as the mass doubles.
It will be the most successful Democratic event, by a factor of three".
This could increase the hydrogen that the algae produce by a factor of three.
The concentration of cGMP that opened half the channels was often lowered by a factor of three or more.
For best results, this initial guess should be within about a factor of three of the actual source size.
Study shows carpooling apps could reduce congestion by a factor of three while still serving the same number of people.
In general, researchers have found that doctors tend to overestimate patient survival by a factor of three to five.
The boiling points of the rare-earth metals vary by nearly a factor of three.
Similar(1)
The corresponding bulk yield strength (compression) of micron-Ni is, about a factor-of-three smaller than the nano-Ni.
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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