what is a perfect number?
GeneralClass 12AllAnswered 27 Mar 2026
Answer
A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself. Proper divisors are positive integers other than the number itself that divide the number evenly.
The smallest perfect number is 6, and here's how it works:
- The divisors of 6 are 1, 2, and 3.
- The sum of these divisors is 1 + 2 + 3 = 6.
Therefore, 6 is a perfect number. Another example is 28:
- The divisors of 28 are 1, 2, 4, 7, and 14.
- The sum of these divisors is 1 + 2 + 4 + 7 + 14 = 28.
Perfect numbers have been studied for centuries, and while there are infinitely many perfect numbers, they become less frequent as you move to larger numbers. The discovery and understanding of perfect numbers date back to ancient Greek mathematicians, such as Euclid. Perfect numbers are closely connected to a specific class of numbers known as Mersenne primes.
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