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

It was a shift in mood as Maresca said earlier in April that the frontman was his "perfect number nine" and wanted "a copy of Nico" rather than to replace him.

From BBC • Sep. 1, 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

Matsuyama switched to a 3-wood off the tee and had 276 yards to the flag, a perfect number for a high, cut 3-wood.

From Seattle Times • Jan. 16, 2022

For in units S is a perfect number, as having a beginning, middle, and end.

From Arguments Of Celsus, Porphyry, And The Emperor Julian, Against The Christians Also Extracts from Diodorus Siculus, Josephus, and Tacitus, Relating to the Jews, Together with an Appendix by Taylor, Thomas