Python Program to Check if a Number is Perfect

Introduction

A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding itself. For example, 6 is a perfect number because its divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. This tutorial will guide you through creating a Python program that checks whether a given number is a perfect number.

Example:

Input: 28
Output: 28 is a perfect number
Input: 10
Output: 10 is not a perfect number

Problem Statement

Create a Python program that:

Takes a number as input.
Checks if the number is a perfect number.
Displays whether the number is perfect or not.

Solution Steps

Take Input from the User: Use the input() function to get a number from the user.
Convert Input to an Integer: Convert the input string to an integer using int().
Find the Proper Divisors: Iterate through all numbers from 1 to half of the given number, and find the divisors.
Calculate the Sum of Divisors: Sum all the proper divisors.
Check if the Sum Equals the Original Number: Compare the calculated sum to the original number.
Display the Result: Use the print() function to display whether the number is a perfect number.

Python Program

# Python Program to Check if a Number is Perfect
# Author: https://www.rameshfadatare.com/

# Step 1: Take input from the user
num = int(input("Enter a number: "))

# Step 2: Find the proper divisors and calculate their sum
sum_of_divisors = sum(i for i in range(1, num) if num % i == 0)

# Step 3: Check if the sum equals the original number
if sum_of_divisors == num and num != 0:
    print(f"{num} is a perfect number")
else:
    print(f"{num} is not a perfect number")

Explanation

Step 1: Take Input from the User

The input() function prompts the user to enter a number. The input is converted to an integer using int().

Step 2: Find the Proper Divisors and Calculate Their Sum

The program iterates over all numbers from 1 to num-1, checking if each is a divisor of num. The proper divisors are summed using a generator expression within the sum() function.

Step 3: Check if the Sum Equals the Original Number

The program checks if the sum of the proper divisors is equal to the original number. If they are equal, the number is a perfect number.

Step 4: Display the Result

The print() function is used to display whether the number is a perfect number.

Output Example

Example 1:

Enter a number: 28
28 is a perfect number

Example 2:

Enter a number: 10
10 is not a perfect number

Example 3:

Enter a number: 6
6 is a perfect number

Conclusion

This Python program demonstrates how to check whether a number is a perfect number by calculating the sum of its proper divisors. It’s a useful exercise for understanding loops, conditionals, and mathematical concepts in Python.