# perfect number

perfect number
noun
: an integer (as 6) the sum of whose divisors including 1 but excluding itself is equal to itself

28, which . 1 + 2 + 4 + 7 + 14, is a perfect number

— compare imperfect number

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Math.
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. Cf. abundant number, deficient number.
[1350-1400; ME]

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perfect number noun (mathematics)
A number equal to the sum of its factors (including unity), as 6=1+2+3 and 28=1+2+4+7+14
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Main Entry:perfect

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perfect number,
a positive integer which is equal to the sum of its factors (other than itself). Six, being the sum of its factors 1, 2, and 3, is a perfect number, as is 28 (1, 2, 4, 7, and 14).

Useful english dictionary. 2012.

### Look at other dictionaries:

• Perfect number — Perfect Per fect, a. [OE. parfit, OF. parfit, parfet, parfait, F. parfait, L. perfectus, p. p. of perficere to carry to the end, to perform, finish, perfect; per (see {Per }) + facere to make, do. See {Fact}.] 1. Brought to consummation or… …   The Collaborative International Dictionary of English

• perfect number — n. a positive integer which is equal to the sum of all its factors, excluding itself: the first four perfect numbers are 6, 28, 496, and 8,128 …   English World dictionary

• Perfect number — In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect… …   Wikipedia

• perfect number — Math. 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. Cf. abundant number, deficient number. [1350 1400; ME] * * * ▪ mathematics       a positive… …   Universalium

• perfect number — noun A number that is the sum of all of its divisors except itself. The factors of 6 are 1, 2, 3 and 6, and 1 + 2 + 3 = 6, so 6 is a perfect number …   Wiktionary

• perfect number — per′fect num′ber n. math. 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 • Etymology: 1350–1400 …   From formal English to slang

• perfect number — /pɜfəkt ˈnʌmbə/ (say perfuhkt numbuh) noun a number which is equal to the sum of its aliquot parts …

• perfect number — noun Date: 14th century an integer (as 6 or 28) the sum of whose integral factors including 1 but excluding itself is equal to itself …   New Collegiate Dictionary

• Multiply perfect number — In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is called k perfect (or k fold perfect) if and only if the sum of… …   Wikipedia

• Unitary perfect number — A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself. (A divisor d of a number n is a unitary divisor if d and n / d share no common factors.) Some perfect numbers are… …   Wikipedia