Perfect Number Checker
Check if a number is perfect, see all its proper divisors, and find the nearest perfect numbers.
Use the Perfect Number Checker
Enter a Number
Try:
Supports integers from 1 to 10,000,000.
Divisor Analysis
Number
Proper Divisor Sum
Divisor Count (excluding self)
Proper Divisors
Nearby Perfect Numbers
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The first four perfect numbers: 6, 28, 496, 8128.
Summary
A perfect number is a positive integer that equals the sum of its proper divisors (all divisors except itself). For example, 6 is perfect because 1 + 2 + 3 = 6. This tool checks any integer up to 10 million, lists every proper divisor, and identifies the nearest perfect numbers in either direction.
How it works
- Enter a positive integer in the input field.
- The tool computes all proper divisors (divisors less than the number itself).
- It sums those divisors and compares to the original number.
- Numbers where the sum equals the number are perfect; less is deficient; greater is abundant.
- The panel also shows the two nearest perfect numbers to give context.
Use cases
- Verify whether a number is perfect for a math class or homework.
- Explore number theory and the concept of divisor sums.
- Find all factors of a number quickly.
- Teach students the difference between perfect, deficient, and abundant numbers.
- Satisfy curiosity about rare perfect numbers like 496 and 8128.
Frequently Asked Questions
Last updated: 2026-06-11 · Reviewed by Nham Vu