Dictionary of Phrase and Fable—A

An Abundant Number

A number such that the sum of all its divisors (except itself) is greater than the number itself. Thus 12 is an abundant number, because its divisors, 1, 2, 3, 4, 6 = 16, which is greater than 12.

A Deficient number is one of which the sum of all its divisors is less than itself, as 10, the divisors of which are 1, 2, 5 = 8, which is less than 10.

A Perfect number is one of which the sum of all its divisors exactly measures itself, as 6, the divisors of which are 1, 2, 3 = 6.

Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
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