Usually means: Many divisors relative to size.
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We found 4 dictionaries that define the word highly composite number:

General (2 matching dictionaries)
  1. highly composite number: Wiktionary
  2. Highly composite number: Wikipedia, the Free Encyclopedia

Science (2 matching dictionaries)
  1. Highly Composite Number: Eric Weisstein's World of Mathematics
  2. highly composite number: PlanetMath Encyclopedia

Definitions from Wiktionary (highly composite number)

noun:  (number theory) A positive integer that has more divisors than any smaller positive integer.
noun:  Used other than figuratively or idiomatically: see highly, composite number; A positive integer that has a relatively large number of divisors.

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