# 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.

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

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.)