Question

What is a perfect number? Give examples

Answer 1

Hint: The perfect number is a positive integer that is equal to the sum of all its proper divisors, excluding the number itself, as defined in this question. Simply put, a perfect number is one in which the sum of all factors is twice the original number. As a result, we'll need to find all of the supplied numbers' components and see if their sum is twice the given number.

Complete step-by-step solution:
In this given question we are asked to define a perfect number with examples.
A perfect number is a positive integer in which the total of all its proper divisors, excluding the number itself, equals the number itself. Simply said, a number is perfect if the sum of all of its parts is twice.
By considering some of the examples of perfect numbers such as 6 and 28.
Now, we know that the factors of 6 are 1, 2, 3 and 6, the sum of all factors is 12 that is 2 times of 6
Hence, 6 is a perfect number
We know that the factors of 25 are 1, 2, 4, 7, 14 and 28. The sum of all the factors is 56 that is 2 times f 28.
Hence, 28 is a perfect number
Here, above are a few examples of perfect numbers.

Note: The proper divisors or factors are all the divisors of a number except the number itself, as seen here. It is a perfect number when their sum equals the number. For example, the correct divisors of 6 are 1, 2, and 3, and their sum equals 6, making it a perfect number.