What is meant by perfect number in python?

Python Functions: Exercise-11 with Solution

Write a Python function to check whether a number is perfect or not.

According to Wikipedia : In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself).
Example : The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128.

Sample Solution:-

Python Code:

def perfect_number(n):
    sum = 0
    for x in range(1, n):
        if n % x == 0:
            sum += x
    return sum == n
print(perfect_number(6))
 

Sample Output:

True

Pictorial presentation:

Flowchart:

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

Python Code Editor:

Have another way to solve this solution? Contribute your code (and comments) through Disqus.

Previous: Write a Python program to print the even numbers from a given list.
Next: Write a Python function that checks whether a passed string is palindrome or not.

This is a Python Program to check if a number is a Perfect number.

Problem Description

The program takes a number and checks if it is a Perfect number.

Problem Solution

1. Take in an integer and store it in a variable.
2. Initialize a variable to count the sum of the proper divisors to 0.
3. Use a for loop and an if statement to add the proper divisors of the integer to the sum variable.
4. Check if the sum of the proper divisors of the number is equal to the variable.
5. Print the final result.
6. Exit.

Program/Source Code

Here is source code of the Python Program to check if a number is a Perfect number. The program output is also shown below.

 
n = int(input("Enter any number: "))
sum1 = 0
for i in range(1, n):
    if(n % i == 0):
        sum1 = sum1 + i
if (sum1 == n):
    print("The number is a Perfect number!")
else:
    print("The number is not a Perfect number!")

Program Explanation

1. User must enter the number and store it in a variable.
2. Use a for loop to generate numbers from 1 to n (where n is not included as we need the sum of the proper divisors of the number).
3. Using an if statement check if the number divided by i gives the remainder as 0 which is basically the proper divisor of the integer.
4. Then the proper divisors of the number are added to the sum variable.
5. If the sum of the proper divisors of the number is equal to the original number, tje number is a Perfect number.
6. The final result is printed.

Runtime Test Cases

 
Case 1:
Enter any number: 6
The number is a Perfect number!
 
Case 2:
Enter any number: 25
The number is not a Perfect number!

Sanfoundry Global Education & Learning Series – Python Programs.

To practice all Python programs, here is complete set of 150+ Python Problems and Solutions.

Next Steps:

• Get Free Certificate of Merit in Python Programming
• Participate in Python Programming Certification Contest
• Become a Top Ranker in Python Programming
• Take Python Programming Tests
• Chapterwise Practice Tests: Chapter 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
• Chapterwise Mock Tests: Chapter 1, 2, 3, 4, 5, 6, 7, 8, 9, 10