Perfect Number Calculator
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Data Source and Methodology
All calculations are based on the standard definition of perfect numbers in number theory.
The Formula Explained
Sum of divisors = Number, where divisors are all positive divisors excluding the number itself.
Glossary of Terms
- Perfect Number: A number equal to the sum of its proper divisors.
- Divisor: A number that divides another without leaving a remainder.
Example: How It Works
Example: Check if 28 is a perfect number. Divisors are 1, 2, 4, 7, 14. Sum = 1 + 2 + 4 + 7 + 14 = 28. Thus, 28 is a perfect number.
Frequently Asked Questions (FAQ)
What is a perfect number?
A perfect number is a positive integer that equals the sum of its proper positive divisors, excluding the number itself.
What are some examples of perfect numbers?
Examples of perfect numbers include 6, 28, 496, and 8128.
Why are perfect numbers important?
Perfect numbers have been studied for their unique properties and relationships to other areas of mathematics such as prime numbers.
How many perfect numbers are there?
There are infinitely many perfect numbers, but only a few are known. They are rare and become less frequent as numbers get larger.
What is the largest known perfect number?
The largest known perfect number corresponds to the largest known Mersenne prime. As of recent records, one of the largest is 2^77,232,917−1.