s that the aliquot parts of which, taken all together, do not make a sum that is equal to the number itself, but either exceed it or fall short of it; being an abundant imperfect number in the former case, and a defective number in the latter. Thus 12 is an abundant imperfect number, because the sum of all its aliquot parts, 1, 2, 3, 4, 6, makes 16, which exceeds the number 12. And 10 is a defective imperfect number, because its aliquot parts 1, 2, 5, taken all together, make only 8, which is less than the number 10 itself.