An abundant number is a positive integer that has the sum of its proper divisors greater than the number itself. Proper divisors are all the positive divisors of a number, excluding the number itself. For example, the number 12 has proper divisors 1, 2, 3, 4, 6, and their sum is 16, which is greater than 12. Therefore, 12 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 interesting in various mathematical contexts, including perfect numbers and deficient numbers.