What is a Perfect Number in Python? Exploring the Concept and Python Program to Find Them

A perfect number in Python is a number that equals the sum of all its proper divisors, excluding itself. For example, 6 is perfect because its divisors 1, 2, and 3 add up to 6. This concept, rooted in mathematics, is often used in coding challenges to test logic and problem-solving skills. Python makes it simple to check whether a number is perfect through loops, conditions, and functions. 

In this guide, you’ll read more about what makes a number perfect, how the logic works, and different Python programs to find them. You’ll also explore function-based, loop-based, and recursive methods, advanced techniques like list comprehension, performance comparisons, and real-world examples to practice and master this concept. 

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Perfect Number in Python – Step-by-Step Approach 

A perfect number in Python is a number that equals the sum of all its proper divisors (excluding itself). 

 To find one, you can break the problem into small, simple steps. Let’s go through each step with examples and outputs. 

1. Taking Input and Finding Divisors 

Start by asking the user for a number and then find its divisors using a for loop. 

 A divisor is any number that divides the given number completely (remainder = 0). 

Code: 

num = int(input("Enter a number: ")) 
divisors = [] 
 
for i in range(1, num): 
    if num % i == 0: 
        divisors.append(i) 
 
print("Divisors:", divisors) 

Example Input: 

Enter a number: 6 

Output: 

Divisors: [1, 2, 3] 

Explanation: 

 The numbers 1, 2, and 3 divide 6 evenly. These are its proper divisors.  

2. Summing the Divisors 

Once you have the divisors, add them up using Python’s built-in sum() function. 

Code: 

sum_of_divisors = sum(divisors) 
print("Sum of divisors:", sum_of_divisors) 
  

Output: 

Sum of divisors: 6 

Explanation: 

 1 + 2 + 3 = 6, which is equal to the original number. 

Also Read: Python In-Built Function [With Syntax and Examples] 

3. Checking the Perfect Number Condition 

Now, compare the sum of divisors with the original number. 

 If both are equal, it’s a perfect number. 

Code: 

if sum_of_divisors == num: 
    print(num, "is a perfect number") 
else: 
    print(num, "is not a perfect number") 
  

Output: 

6 is a perfect number 

Explanation: 

Since the sum equals the number itself, 6 is perfect. 

Also Read: Top 48 Machine Learning Projects [2025 Edition] with Source Code 

4. Complete Python Program 

Let’s put all the steps together into one complete script. 

Code: 

num = int(input("Enter a number: ")) 
divisors = [] 
 
for i in range(1, num): 
    if num % i == 0: 
        divisors.append(i) 
 
print("Divisors:", divisors) 
print("Sum of divisors:", sum(divisors)) 
 
if sum(divisors) == num: 
    print(num, "is a perfect number") 
else: 
    print(num, "is not a perfect number") 
  

Example Input: 

Enter a number: 28 

Output: 

Divisors: [1, 2, 4, 7, 14] 
Sum of divisors: 28 
28 is a perfect number 

Explanation: 

 When you add up all the divisors of 28, you get 28. That’s why it’s a perfect number. 

5. Example Table 

 6. Visualizing the Process 

Here’s how the logic flows: 

Start 
↓ 
Input a number 
↓ 
Find all divisors 
↓ 
Add them up 
↓ 
Compare with the original number 
↓ 
If equal → Perfect number 
Else → Not perfect 
↓ 
End 
 

7. Key Takeaways 

• A perfect number equals the sum of its proper divisors. 
• Use loops and if conditions to check the logic. 
• Python’s sum() and range() make the process simple. 
• The first few perfect numbers are 6, 28, 496, and 8128. 

This foundational logic can be extended to check perfect numbers within a range or using functions and recursion. 

Also Read: Top 36+ Python Projects for Beginners and Students to Explore in 2025

Perfect Number Program in Python Using Functions 

Using functions in Python makes your program cleaner, reusable, and easier to test. 

 Instead of writing the same code repeatedly, you can define a function that checks whether a number is perfect and then call it whenever needed. 

Let’s see how you can create a perfect number program in Python using functions step by step. 

1. Defining the Function 

Start by defining a function named is_perfect_number() that takes a number as an argument. 

 Inside the function, you’ll calculate the sum of all divisors and compare it with the original number. 

Code: 

def is_perfect_number(num): 
    divisors = [] 
    for i in range(1, num): 
        if num % i == 0: 
            divisors.append(i) 
    return sum(divisors) == num 

Explanation: 

• The function loops from 1 to num - 1. 
• It collects divisors that divide the number evenly. 
• It returns True if the sum of divisors equals the number. 

2. Calling the Function 

You can now call the function with any number and print the result. 

Code: 

number = int(input("Enter a number: ")) 
 
if is_perfect_number(number): 
    print(number, "is a perfect number") 
else: 
    print(number, "is not a perfect number") 
  

Example Input: 

Enter a number: 6 

Output: 

6 is a perfect number 

Explanation: 

 The divisors of 6 are [1, 2, 3], and their sum equals 6. 

 The function returns True, so the message confirms it’s a perfect number. 

Also Read: How to Call a Function in Python? 

3. Displaying Results for Multiple Numbers 

You can also use the same function to check multiple numbers in a loop. 

 This shows the advantage of writing reusable functions. 

Code: 

for n in range(1, 31): 
    if is_perfect_number(n): 
        print(n, "is a perfect number") 
  

Output: 

6 is a perfect number 
28 is a perfect number 

Explanation: 

 The program loops from 1 to 30, checks each number, and prints the perfect ones. 

4. Function-Based Program Summary 

5. Benefits of Using Functions 

• Keeps your code organized and modular. 
• Easier to debug and update later. 
• Can be reused in larger programs. 
• Helps you test multiple numbers quickly. 

6. Visual Flow of Function Logic 

Define function → Input a number → Find divisors → Sum divisors → Return True/False → Print result 

By using functions, you make your perfect number program in Python more structured and maintainable. 

 This approach forms a strong base for building advanced versions, such as using recursion or checking perfect numbers within a range. 

Also Read: Most Important Python Functions [With Examples] | Types of Functions

Perfect Number Program in Python Using While Loop 

Using a while loop to check for perfect numbers in Python is another approach that beginners can try. 

It works similarly to a for loop but gives you more control over the loop counter and conditions. 

This section will show you how to write a perfect number program in Python using while loop with clear examples and outputs. 

1. Initial Setup 

Start by taking input from the user and initializing variables: 

• i to iterate through potential divisors 
• sum_of_divisors to store the sum of all proper divisors 

Code: 

num = int(input("Enter a number: ")) 
i = 1 
sum_of_divisors = 0 
  

Example Input: 

Enter a number: 28 

2. Finding Divisors Using While Loop 

Use a while loop to check each number from 1 to num - 1. 

 Add the number to sum_of_divisors if it divides num completely. 

Code: 

while i < num: 
    if num % i == 0: 
        sum_of_divisors += i 
    i += 1 
 
print("Sum of divisors:", sum_of_divisors) 
  

Output: 

Sum of divisors: 28 

Explanation: 

 The loop checks every number less than 28 and sums the divisors: 1 + 2 + 4 + 7 + 14 = 28. 

3. Checking the Perfect Number Condition 

After calculating the sum of divisors, compare it with the original number. 

Code: 

if sum_of_divisors == num: 
    print(num, "is a perfect number") 
else: 
    print(num, "is not a perfect number") 
  

Output: 

28 is a perfect number 

Explanation: 

 Since the sum equals 28, the program correctly identifies it as a perfect number. 

Also Read: Master Python While Loop Syntax with These Easy Examples! 

4. Complete Program Using While Loop 

Code: 

num = int(input("Enter a number: ")) 
i = 1 
sum_of_divisors = 0 
 
while i < num: 
    if num % i == 0: 
        sum_of_divisors += i 
    i += 1 
 
print("Sum of divisors:", sum_of_divisors) 
 
if sum_of_divisors == num: 
    print(num, "is a perfect number") 
else: 
    print(num, "is not a perfect number") 
  

Example Input: 

Enter a number: 6 

Output: 

Sum of divisors: 6 
6 is a perfect number 

5. Example Table of Inputs and Outputs 

6. Key Points to Remember 

• while loop allows flexible iteration and manual control of the counter. 
• Always initialize the loop variable before the loop. 
• Make sure to increment the counter inside the loop to avoid infinite loops. 
• The logic of finding divisors and summing them remains the same as with a for loop. 

Using a while loop is a simple, clear way to implement a perfect number program in Python. 

 It also helps beginners understand how loops work and how conditions can be combined to solve problems efficiently. 

Also Read: Enhance Your Python Skills: 10 Python Projects You Need to Try! 

Perfect Number Program in Python Using Recursion 

Recursion is a technique in Python where a function calls itself to solve a problem. 

You can use recursion to check for perfect numbers in a clean and elegant way. 

This approach helps you understand function calls and how logic can repeat automatically. 

1. Understanding the Logic 

To check a perfect number using recursion, you need: 

• A function that sums all divisors of a number. 
• A base case to stop the recursion. 
• A final comparison to see if the sum equals the original number. 

Steps in simple terms: 

• Start from 1 and check if it divides the number. 
• Add the divisor to a running sum. 
• Call the function again with the next number. 
• Stop when the counter reaches the number itself. 

2. Recursive Function to Sum Divisors 

Code: 

def sum_of_divisors(num, i=1): 
    if i == num: 
        return 0 
    if num % i == 0: 
        return i + sum_of_divisors(num, i + 1) 
    else: 
        return sum_of_divisors(num, i + 1) 
  

Explanation: 

• num is the number to check. 
• i starts at 1 and increases with each call. 
• If i divides num, add it to the sum returned by the next recursive call. 
• Stop recursion when i equals num. 

Also Read: Top 40 Pattern Programs in Python to Master Loops and Recursion 

3. Checking the Perfect Number 

Once the sum of divisors is calculated recursively, compare it with the original number. 

Code: 

number = int(input("Enter a number: ")) 
if sum_of_divisors(number) == number: 
    print(number, "is a perfect number") 
else: 
    print(number, "is not a perfect number") 

Example Input: 

Enter a number: 28 

Output: 

28 is a perfect number 

Explanation: 

 The recursive function calculates 1 + 2 + 4 + 7 + 14 = 28. 

 Since the sum equals the original number, it’s perfect. 

4. Complete Program Using Recursion 

Code: 

def sum_of_divisors(num, i=1): 
    if i == num: 
        return 0 
    if num % i == 0: 
        return i + sum_of_divisors(num, i + 1) 
    else: 
        return sum_of_divisors(num, i + 1) 
 
number = int(input("Enter a number: ")) 
 
print("Sum of divisors:", sum_of_divisors(number)) 
 
if sum_of_divisors(number) == number: 
    print(number, "is a perfect number") 
else: 
    print(number, "is not a perfect number") 
  

Example Input: 

Enter a number: 6 

Output: 

Sum of divisors: 6 
6 is a perfect number 

5. Example Table of Inputs and Outputs 

6. Key Takeaways 

• Recursion simplifies the logic by eliminating explicit loops. 
• The base case (i == num) is crucial to stop recursion. 
• Perfect numbers like 6, 28, and 496 can be checked efficiently. 
• This method is helpful for understanding function calls and problem-solving in Python. 

Using recursion for a perfect number program in Python demonstrates a different approach compared to loops and makes your code concise and readable. 

Also Read: GitHub Project on Python: 30 Python Projects You’d Enjoy

Advanced Approaches to Find Perfect Numbers 

Once you understand basic methods, you can explore advanced ways to find perfect numbers in Python. 

These approaches make your code cleaner, more Pythonic, and sometimes more efficient. 

1. Using List Comprehension 

Python’s list comprehension allows you to calculate divisors and their sum in a single line. 

Code: 

num = int(input("Enter a number: ")) 
sum_of_divisors = sum([i for i in range(1, num) if num % i == 0]) 
 
if sum_of_divisors == num: 
    print(num, "is a perfect number") 
else: 
    print(num, "is not a perfect number") 
  

Example Input: 

Enter a number: 28 

Output: 

28 is a perfect number 

Why it works: 

The list comprehension [i for i in range(1, num) if num % i == 0] generates all divisors efficiently. 

Then sum() adds them, and the result is compared with the number. 

2. Using Lambda and Filter Functions 

You can use lambda and filter() to find divisors without explicit loops. 

Code: 

num = int(input("Enter a number: ")) 
divisors = list(filter(lambda x: num % x == 0, range(1, num))) 
sum_of_divisors = sum(divisors) 
 
if sum_of_divisors == num: 
    print(num, "is a perfect number") 
else: 
    print(num, "is not a perfect number") 
  

Example Input: 

Enter a number: 6 

Output: 

6 is a perfect number 

Explanation: 

filter() selects numbers that divide num evenly. 

sum() calculates the total, and the check confirms perfection. 

Also Read: Lambda and Anonymous Function in Python 

3. Using Object-Oriented Programming (OOP) 

You can encapsulate the logic in a class for reusable and organized code. 

Code: 

class PerfectNumber: 
    def __init__(self, num): 
        self.num = num 
 
    def divisors_sum(self): 
        return sum([i for i in range(1, self.num) if self.num % i == 0]) 
 
    def check_perfect(self): 
        return self.divisors_sum() == self.num 
 
number = int(input("Enter a number: ")) 
pn = PerfectNumber(number) 
 
if pn.check_perfect(): 
    print(number, "is a perfect number") 
else: 
    print(number, "is not a perfect number") 
  

Example Input: 

Enter a number: 28 

Output: 

28 is a perfect number 

Benefits of OOP Approach: 

• Organizes logic into methods for clarity. 
• Makes it easy to reuse and extend. 
• Good for projects with multiple number checks. 

Key Takeaways 

• List comprehension and lambda-filter methods make your perfect number program in Python concise. 
• OOP approach structures your code for readability and reuse. 
• Advanced approaches help you practice Pythonic coding while checking for perfect numbers efficiently. 

Checking for Perfect Numbers in a Given Range 

Sometimes, you might want to find all perfect numbers within a specific range instead of checking just one number. 

 Python makes this easy by combining loops with the logic for a perfect number program in Python. 

1. Using a For Loop 

You can iterate through a range of numbers and check each number individually. 

Code: 

start = int(input("Enter start of range: ")) 
end = int(input("Enter end of range: ")) 
 
for num in range(start, end + 1): 
    sum_of_divisors = sum([i for i in range(1, num) if num % i == 0]) 
    if sum_of_divisors == num: 
        print(num, "is a perfect number") 

Example Input: 

Enter start of range: 1 
Enter end of range: 100 

Output: 

6 is a perfect number 
28 is a perfect number 

Explanation: 

• The loop checks every number from 1 to 100. 
• For each number, it calculates the sum of divisors. 
• If the sum equals the number, it prints the number as perfect. 

2. Using a Function for Reusability 

You can also define a function to check perfect numbers and call it within the range loop. 

Code: 

def is_perfect(num): 
    return sum([i for i in range(1, num) if num % i == 0]) == num 
start = 1 
end = 100 
 
for n in range(start, end + 1): 
    if is_perfect(n): 
        print(n, "is a perfect number") 
  

Output: 

6 is a perfect number 
28 is a perfect number 

Benefits of Using a Function: 

• Makes the code cleaner and more organized. 
• The logic for checking a perfect number is reusable. 
• Easier to expand the range or use in other programs. 

You may also Read: Free Python Course with Certificate 

3. Example Table of Perfect Numbers in a Range 

Key Takeaways 

• Checking for perfect numbers in a range uses the same logic as single-number checking. 
• Loops and list comprehensions make it easy to calculate divisors for multiple numbers. 
• Using a function improves code readability and reusability. 

This approach is helpful when you want to find all perfect numbers in Python for exercises, projects, or coding challenges.

Perfect Numbers vs. Perfect Squares: A Clear Distinction

Though both are mathematically 'perfect,' perfect numbers and perfect squares differ significantly in their fundamental structure, frequency, and the computational complexity involved in their identification. Understanding these distinctions is key to appreciating their unique places in number theory.

The key distinction between perfect numbers and perfect squares boils down to this:

• Perfect Squares: These are born from multiplication, an integer multiplied by itself.
• Perfect Numbers: These are defined by addition, which is the sum of their proper divisors.

To further illustrate the differences, consider the following table:

In essence, while both terms involve a special property of integers, the nature of that property—multiplicative for perfect squares and additive for perfect numbers—sets them distinctly apart. Perfect squares are easily generated and verified, unlike the computationally expensive perfect number in Python. Understanding this difference is crucial when exploring various classifications and characteristics within number theory.

Also Read: Python Tutorial: Setting Up, Tools, Features, Applications, Benefits

Let's now consider the practical aspects of identifying perfect number in Python and perfect squares in Python. The following section will explore the computational considerations of finding these elusive numbers.

How Can upGrad's Courses Propel Your Journey Beyond Perfect Numbers with Python? 

So far, we have shown how understanding perfect numbers, while a specific mathematical concept, plays an integral part in demonstrating core programming principles like iteration, conditional logic, and algorithmic thinking. In Python, you can find perfect numbers by iterating through integers, identifying their divisors, and checking if their sum equals the original number.  

upGrad empowers your Python journey beyond exploring concepts like perfect number program in Python to building a successful career. A leading online learning platform, upGrad boasts over 10 million learners, 200+ courses, and 1,400+ hiring partners.  

In India, upGrad offers the following Python-related courses.   

• Free Learn Python Programming Course Online with Certificates 

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