Deficient Number

Pronunciation: /də.fɪ.ʃɪnt nʌm.bər/ Explain

A deficient number is an integer such that the sum of its proper divisors is less than the number itself. For example, 12 is a deficient number. The proper divisors of 12 are 1, 3, 4. The sum of the proper divisors is 1 + 3 + 4 = 8. 8 < 12 so 12 is a deficient number.

All prime numbers are deficient. The only proper divisor of a prime number is 1. The sum of 1 is 1, which is less than the prime number.


  1. McAdams, David E.. All Math Words Dictionary, deficient number. 2nd Classroom edition 20150108-4799968. pg 56. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Deficient Number. 4/19/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

4/19/2019: Updated equations and expressions to the new format (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
6/18/2018: Initial version. (McAdams, David E.)

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