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In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
Feb 22, 2024 · Learn what perfect numbers are, how to find them, and their connection to Mersenne primes. See the list of all 51 perfect numbers and their divisors, and the history of their study.
Learn what are perfect numbers, how to find them, and their history and properties. See examples, questions and solutions on perfect numbers in maths.
- 5 min
- A perfect number is defined as a positive integer which is equal to the sum of its positive divisors, excluding the number itself.
- The smallest perfect number is 6, which is the sum of 1, 2, and 3.
- There are around 51 known perfect numbers. There are only 2 perfect numbers from 1 to 100 which are 6 and 28. The latest perfect number was discove...
- The first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.
Learn what perfect numbers are, how to find them, and their history and properties. Perfect numbers are positive integers that are equal to the sum of their factors, excluding themselves.
A perfect number is defined as a positive integer that can be expressed as the sum of its proper factors (factors except for the number itself). Perfect number examples: 6, 28, 496. The factors of 6 are 1, 2, 3 and 6. We can write 6 = 1 + 2 + 3 . The smallest perfect number is 6.
- A perfect square is a number, which can be expressed as the square of a number from the same number system whereas a perfect number is a number, wh...
- The perfect numbers found till date have been even. There is no evidence of odd perfect numbers.
- So far, 51 perfect numbers are known till date.
- A perfect number can be written as the sum of its proper factors. The only factor of 1 is 1. So, 1 is not a perfect number.
- The first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.
6 days ago · Perfect numbers are positive integers n such that n=s(n), (1) where s(n) is the restricted divisor function (i.e., the sum of proper divisors of n), or equivalently sigma(n)=2n, (2) where sigma(n) is the divisor function (i.e., the sum of divisors of n including n itself). For example, the first few perfect numbers are 6, 28, 496 ...
Learn what a perfect number is, how to find them, and why they are interesting. Explore the Euclid-Euler theorem, the largest known perfect number, and some open questions about perfect numbers.
