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The phrase "a number of smaller" is correct and usable in written English.
It can be used when referring to several smaller items or components within a larger context.
Example: "The project will be divided into a number of smaller tasks to make it more manageable."
Alternatives: "several smaller" or "a variety of smaller".
Exact(58)
A number of smaller software companies are doing similar things.
There are also a number of smaller awards.
A number of smaller items are still being negotiated.
Read also made a number of smaller bequests.
While Silk Road no longer exists, a number of smaller outfits offer the same services.
A number of smaller companies are also attempting to hold their own against Comixology's dominance.
The museum's permanent collection comprises roughly 40 large signs and a number of smaller objects.
It contains a topographical map covering a number of smaller peaks and trails.
"They also are in a number of smaller enclaves spotted all around the country.
A number of smaller shopping centres have fallen victim to the credit crunch.
It will cost less to maintain a single centralised office than a number of smaller offices.
More suggestions(16)
a number of weaker
a multitude of smaller
a number of poorer
a number of narrower
a breakdown of smaller
a number of minor
a number of earlier
a number of lighter
a number of less
a number of slimmer
a number of faster
a number of small sized
a number of cooler
a number of lower
a number of slower
a meal of smaller
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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