Perfect Number Checker Calculator

Test numbers using divisor sums and factor analysis. Review parity, primes, and Euclid insights today. Get accurate checks, exports, examples, formulas, and guided usage.

Calculator Inputs

Example Data Table

Number Proper Divisors Sum Classification
6 1, 2, 3 6 Perfect
12 1, 2, 3, 4, 6 16 Abundant
15 1, 3, 5 9 Deficient
28 1, 2, 4, 7, 14 28 Perfect
496 1, 2, 4, 8, 16, 31, 62, 124, 248 496 Perfect

Formula Used

Perfect number rule: A number is perfect when the sum of its proper divisors equals the number itself.

Core test: Perfect if s(n) = n, where s(n) is the sum of proper divisors.

Relation with sigma: Since σ(n) includes the number itself, a perfect number also satisfies σ(n) = 2n.

Euclid-Euler form: Every even perfect number has the form 2^(p−1) × (2^p − 1) where 2^p − 1 is prime.

How to Use This Calculator

  1. Enter a positive whole number in the input box.
  2. Select whether to show divisors, factorization, and sigma output.
  3. Press Check Number to calculate the result.
  4. Read the result panel above the form for classification.
  5. Use the export buttons to save the result as CSV or PDF.

Related Calculators

Modular Exponentiation Fast Power CalculatorReverse Euclidean algorithm calculatorfast modular exponentiation calculatorLarge number modulo calculatormodular congruence solverpisano period calculatoreuler totient calculatorlegendre symbol calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.