Perfect Number Checker
Check a Number
Check if a number is perfect, abundant, or deficient
Find Perfect Numbers
Find all perfect numbers up to a given limit using Mersenne primes
Amicable Number Pair Check
Check if two numbers form an amicable pair
Formula
Perfect: σ(n) - n = n | Abundant: σ(n) - n > n | Deficient: σ(n) - n < n | Even perfect: 2^(p-1) × (2^p - 1)
Frequently Asked Questions
What is a perfect number?
A perfect number equals the sum of its proper divisors (all divisors except itself). The first few perfect numbers are 6 (1+2+3), 28 (1+2+4+7+14), 496, and 8128. All known perfect numbers are even.
What are amicable numbers?
Two numbers are amicable if the sum of proper divisors of each equals the other number. The smallest amicable pair is (220, 284): the divisors of 220 sum to 284, and the divisors of 284 sum to 220.
What is the difference between abundant and deficient?
An abundant number has divisors that sum to more than itself (e.g., 12: 1+2+3+4+6=16 > 12). A deficient number has divisors that sum to less (e.g., 8: 1+2+4=7 < 8). A perfect number is exactly equal.
You may also need
+
Factorial Calculator
Free factorial calculator. Calculate n! (n factorial), double factorial, and subfactorial for any positive integer.
Math+
LCM & GCD Calculator
Free LCM and GCD calculator. Find the Least Common Multiple and Greatest Common Divisor of two or more numbers.
Math+
Prime Counting Function Calculator
Free prime counting function calculator. Count the number of primes up to N, find the Nth prime, and explore prime density using π(x).
Math