Perfect Number Calculator

Use our free perfect number calculator to test if a number is perfect (sum of proper divisors equals the number), search a range, or list the first n perfect numbers.

Math

Mode

Number

Start

End

How Many

Formula

A perfect number is a positive integer where the sum of its proper divisors equals the number itself. Example: 28 = 1+2+4+7+14. Also classifies numbers as deficient or abundant.

A perfect number equals the sum of its proper divisors (excluding itself).

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select a mode.
2Check: enter a number to test.
3Range: enter start and end to find perfect numbers.
4First n: enter count (1–8) to see the first perfect numbers.
5Click Calculate.

Examples

Check 28

1.Proper divisors: 1,2,4,7,14
2.Sum = 28 = 28 → Perfect!

Result: Perfect

Check 12

1.Proper divisors: 1,2,3,4,6
2.Sum = 16 > 12 → Abundant

Result: Abundant

Range 1-10000

1.Perfect numbers: 6, 28, 496, 8128

Result: 4 found

Frequently Asked Questions

A number where sum of proper divisors equals the number.

6, 28, 496, 8128, 33550336, ... (all known are even).

None are known. It remains an open problem in mathematics.

Deficient: sum < number. Abundant: sum > number.

Even perfect numbers are of the form 2^(p-1)(2^p-1) where 2^p-1 is prime (Mersenne prime).

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CalculateMe Team

Last updated: 2026-07-14

Perfect Number Calculator

Formula

How It Works

Examples

Check 28

Check 12

Range 1-10000

Frequently Asked Questions

What is a perfect number?

What are the first few?

Are there odd perfect numbers?

What are deficient/abundant?

Euclid-Euler theorem?

Related Calculators

Perfect Number Calculator

Formula

How It Works

Examples

Check 28

Check 12

Range 1-10000

Frequently Asked Questions

What is a perfect number?

What are the first few?

Are there odd perfect numbers?

What are deficient/abundant?

Euclid-Euler theorem?

Related Calculators