Abundant number
![Demonstration, with Cuisenaire rods, of the abundance of the number 12](/Images/godic/202412/19/Abundant_number_Cuisenaire_rods_121300.png")
![](/Images/godic/202412/19/Lattice_of_the_divisibility_of_60.svg1300.png")
In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.