Número Perfeito?
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
perfeito se σ(n)−n = n
About this calculator
This calculator checks if a natural number is perfect. A number is perfect when the sum of its proper divisors (all positive divisors except itself) equals the number itself. For example, 6 is perfect because its proper divisors (1, 2, 3) sum to 6. The tool also displays the proper divisors and their sum, making verification easy.
The operation is simple: you enter a positive integer and the calculator finds all its proper divisors, calculates their sum, and compares it to the original number. If the sum equals the number, it is classified as perfect. Otherwise, the sum and the difference are shown. The calculation iterates up to the square root of the number for efficiency.
Use this calculator to explore mathematical properties, verify number theory exercises, or out of curiosity. Perfect numbers are rare and fascinating, with applications in cryptography and recreational math. It is useful for students, teachers, and enthusiasts who want to confirm if a number is perfect without manual computation.
Caution: The calculator only accepts positive integers. Very large numbers may take time to process, as the algorithm checks divisors up to the square root. For numbers above 10^9, patience or advanced methods are recommended. Also, zero and negative numbers are not considered perfect.
Frequently asked questions
What are proper divisors?
They are all positive divisors of a number, excluding the number itself. For example, the proper divisors of 6 are 1, 2, and 3.
Are there any odd perfect numbers?
To date, no odd perfect number has been found. It is believed they do not exist, but this has not been mathematically proven.
What is the next perfect number after 6?
The next perfect number is 28 (proper divisors: 1, 2, 4, 7, 14; sum 28). Then come 496, 8128, and 33550336.
Does the calculator work for negative numbers?
No. The calculator only accepts positive integers, as the definition of perfect numbers applies only to natural numbers.
Why does my large number take time to compute?
The algorithm checks divisors up to the square root of the number. For very large numbers, this may take a few seconds. Please be patient or use smaller numbers.