Perfect Number Program in Python – Explained with Examples

In this blog post, we'll explore:

• 1. What is a perfect number?
   
• 2. How to check if a number is perfect
   
• 3. A step-by-step Python program
   
• 4. Examples and edge cases
   
• 5. How to write cleaner, optimized code
   
• 6. Where you can learn such problems in depth (Hint: Uncodemy’s Python Programming Course)
   

Let’s begin!

✅ What is a Perfect Number?

A perfect number is a positive integer that is equal to the sum of its proper positive divisors, excluding itself.

🔍 Definition:

A number n is perfect if:
 n = sum of all its divisors (excluding n itself)

🔢 Examples:

• a. 6
     Divisors: 1, 2, 3
     Sum: 1 + 2 + 3 = 6 ✅ Perfect
   
• b. 28
     Divisors: 1, 2, 4, 7, 14
     Sum: 1 + 2 + 4 + 7 + 14 = 28 ✅ Perfect
   
• c. 12
     Divisors: 1, 2, 3, 4, 6
     Sum: 1 + 2 + 3 + 4 + 6 = 16 ❌ Not Perfect
   

Perfect numbers are rare and fascinating—they're tied to ancient mathematics and even cryptographic theories!

🧮 Perfect Number Logic in Python

To check whether a number is perfect, follow this logic:

1. Take a number n

2. Loop from 1 to n-1

3. For each number i, check if it divides n (i.e., n % i == 0)

4. Sum up all such i

5. If the sum equals n, then it’s perfect

💻 Python Program to Check Perfect Number

Let’s write the complete Python program step by step.

✅ Code:

python

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# Perfect Number Program in Python

def is_perfect(number):

    if number < 1:

        return False

    sum_of_divisors = 0

    for i in range(1, number):

        if number % i == 0:

            sum_of_divisors += i

    return sum_of_divisors == number

# Taking input from user

num = int(input("Enter a number: "))

if is_perfect(num):

    print(f"{num} is a Perfect Number ✅")

else:

    print(f"{num} is NOT a Perfect Number ❌")

🧾 Sample Output:

less

CopyEdit

Enter a number: 28

28 is a Perfect Number ✅

🧠 How It Works – Code Explained

Let’s break the logic:

• 1. We define a function is_perfect()
   
• 2. Loop through all numbers from 1 to n-1
   
• 3. Check if the current number divides n without a remainder
   
• 4. Add it to the sum_of_divisors
   
• 5. Finally, compare the sum to the original number

🛠️ Bonus Tip:

You can reduce time complexity by looping only till n // 2. Why? No divisor (except n itself) can be more than half of n.

python

CopyEdit

for i in range(1, number // 2 + 1):

📈 Optimized Version of the Program

python

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def is_perfect(number):

    if number < 2:

        return False

    sum_of_divisors = 1  # Start with 1 as it's always a divisor

    for i in range(2, number // 2 + 1):

        if number % i == 0:

            sum_of_divisors += i

    return sum_of_divisors == number

This version improves performance slightly, especially for larger numbers.

🧪 Test Cases

❗ Edge Cases to Consider

• 1. Negative numbers ❌
   
• 2. 0 or 1 ❌
   
• 3. Very large numbers (optimization needed) ⚙️
   

Perfect numbers are rare—only a few exist under 10,000.

🧮 List of Known Perfect Numbers (Below 10000)

1. 6

2. 28

3. 496

4. 8128

Want to print all perfect numbers in a given range? Let’s write a loop!

🔄 Find All Perfect Numbers in a Range

python

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def is_perfect(n):

    if n < 2:

        return False

    total = 1

    for i in range(2, n // 2 + 1):

        if n % i == 0:

            total += i

    return total == n

# Find perfect numbers from 1 to 10000

for num in range(1, 10001):

    if is_perfect(num):

        print(num, "is a Perfect Number")

Output:

csharp

CopyEdit

6 is a Perfect Number  

28 is a Perfect Number  

496 is a Perfect Number  

8128 is a Perfect Number

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Solving problems like perfect number programs is an important part of Python learning. But to truly build confidence, you need more structured learning, regular practice, and expert guidance.

That’s why we recommend the Python Programming Course by Uncodemy.

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📝 Final Thoughts

The Perfect Number Program in Python is more than a coding challenge—it's a practical way to learn:

• 1. Divisors and modulus operator
   
• 2. Looping and conditional logic
   
• 3. Functions and return values
   
• 4. Optimizing code with math
   

Now that you know how to write and optimize a perfect number checker, take this further—modify it, enhance it, and most importantly, keep experimenting.

And when you’re ready to master Python beyond the basics, Uncodemy’s expert-led course is just a click away.

Happy Coding! 🐍