perfect number

American  

noun

Mathematics.

1. a positive number that is equal to the sum of all positive integers that are submultiples of it, as 6, which is equal to the sum of 1, 2, and 3.

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perfect number British  

noun

1. an integer, such as 28, that is equal to the sum of all its possible factors, excluding itself

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perfect number Scientific  

1. A positive integer that equals the sum of all of its divisors other than itself. An example is 28, whose divisors (not counting itself) are 1, 2, 4, 7, and 14, which added together give 28.

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Etymology

Origin of perfect number

Middle English word dating back to 1350–1400

Example Sentences

Six is a perfect number, and seven is a prime number, but only a glutton for punishment would put them together in front of a bunch of 13-year-olds.

From The Wall Street Journal • Oct. 14, 2025

“There is no perfect number to send, no perfect geography to send it out to,” Galperin said.

From Los Angeles Times • Jan. 24, 2025

"Without the scientific study, it can’t be said what will be the perfect number for Mount Everest," he said.

From BBC • Jun. 6, 2024

"In light of the weekend's events, I don't think it could have been a more perfect number."

From Reuters • Mar. 14, 2023

Thousand is a perfect number, and no number extends beyond it.

From The Homilies of the Anglo-Saxon Church Containing the Sermones Catholici, or Homilies of ?lfric, in the Original Anglo-Saxon, with an English Version. Volume I. by Aelfric, Abbot of Eynsham