An abundant number is a positive integer that has the sum of its proper divisors greater than itself. Proper divisors are the positive divisors of a number excluding the number itself. For example, the number 12 has proper divisors 1, 2, 3, 4, and 6, which add up to 16. Since 16 is greater than 12, it is classified as an abundant number. Abundant numbers are part of number theory, a branch of mathematics that studies the properties and relationships of numbers. The smallest abundant number is 12, and other examples include 18, 20, and 24. These numbers are significant in various mathematical contexts, including the study of perfect and deficient numbers.