# Abundant Number

Pronunciation: /əˈbʌn.dənt ˈnʌm.bər/ Explain

An abundant number is a positive integer that is less than the sum of its proper divisors. A proper divisor is a divisor of an integer that is not the integer itself. For example, 12 is an abundant number since 12 < 1 + 2 + 3 + 4 + 6 = 16.

Each positive integer is either a deficient number, a perfect number, or an abundant number. A deficient number is greater than the sum of its proper divisors. A perfect number is equal to the sum of its proper divisors. An abundant number is greater than the sum of its proper divisors.

### References

1. McAdams, David E.. All Math Words Dictionary, abundant number. 2nd Classroom edition 20150108-4799968. pg 9. Life is a Story Problem LLC. January 8, 2015. Buy the book

### Cite this article as:

McAdams, David E. Abundant Number. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/abundantnumber.html.

### Revision History

4/11/2019: Changed equations and expressions to new format. (McAdams, David E.)
1/7/2019: Corrected punctuation. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/12/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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