How Many Perfect Numbers are there Between 1 and 100?
source link: https://www.geeksforgeeks.org/how-many-perfect-numbers-are-there-between-1-to-100/
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How Many Perfect Numbers are there Between 1 and 100?
Between 1 and 100, there are two perfect numbers, namely 6 and 28.
Let’s examine the two perfect numbers between 1 and 100:
Perfect Number 6:
The divisors of 6 are 1, 2, and 3.
The sum of these divisors (excluding 6 itself) is 1+2+3=6.
Therefore, 6 is a perfect number.
Perfect Number 28:
The divisors of 28 are 1, 2, 4, 7, and 14.
The sum of these divisors (excluding 28 itself) is 1+2+4+7+14=28.
Therefore, 28 is also a perfect number.
Perfect numbers are relatively rare, and the discovery of more perfect numbers becomes increasingly challenging. Euler proved that if 2p−1 is a prime number, then 2p−1(2p − 1) is a perfect number, where p is a prime number. The known perfect numbers follow this formula, with 6 corresponding to 22(23 − 1) and 28 corresponding to 23(24 − 1).
In the range from 1 to 100, these are the only two known perfect numbers, and they have been known since ancient times.
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