Last updated October 5, 2026 · Report an error
A perfect number is one whose proper divisors (every divisor except the number itself) add up to exactly the number — a rare and famous property that only a handful of small numbers satisfy, like 6 (1+2+3=6) and 28 (1+2+4+7+14=28).
This checker finds a number's proper divisors, sums them, and classifies it as perfect, abundant, or deficient.
How it works
Enter a whole number. The checker finds every proper divisor (excluding the number itself), sums them, and compares that sum to the original number to classify it as perfect (equal), abundant (sum is greater), or deficient (sum is less).
- Enter number.
- Click Calculate to see your results.
Examples
28 is perfect
28's proper divisors are 1, 2, 4, 7, and 14, which sum to exactly 28 — making it a perfect number.
Who should use it
- Checking perfect number coursework for a number theory class.
- Exploring which numbers are abundant, deficient, or perfect for a math enrichment project.
Industry applications
- Number theory and mathematics education
- Recreational mathematics
Advantages
- Classifies any number as perfect, abundant, or deficient in one step.
- Shows the actual proper divisors used in the calculation.
Limitations
- Very large numbers with large prime factors can take noticeably longer to check.
Common mistakes to avoid
- Including the number itself when summing its divisors — perfect number classification specifically uses only proper divisors (excluding the number itself).
- Assuming perfect numbers are common — they're actually extremely rare, with only a handful known even among enormous numbers.
Best practices
- Remember that every prime number is automatically deficient, since a prime's only proper divisor is 1, which is always less than the prime itself (for primes greater than 1).
Tips
- Every known perfect number is even, and follows the pattern 2^(p-1) × (2^p - 1) where 2^p - 1 is a Mersenne prime — whether an odd perfect number can exist at all remains an unsolved problem in mathematics.