Recently, I was working on a small project where I needed to check if a number was a perfect number.
At first, I thought Python might have a built-in function for this. But just like Excel doesn’t have a direct way to filter strikethrough cells, Python doesn’t come with a ready-made tool for perfect numbers. So, I had to write my own program.
In this tutorial, I’ll show you how I solved it. I’ll walk you through three simple methods: using loops, functions, and recursion.
Let’s dive in!
What is a Perfect Number?
A perfect number is a positive integer that equals the sum of its proper divisors (excluding itself).
For example:
- 6 → Divisors are 1, 2, 3 → 1 + 2 + 3 = 6
- 28 → Divisors are 1, 2, 4, 7, 14 → 1 + 2 + 4 + 7 + 14 = 28
Method 1 – Program to Find a Perfect Number Using Loops
When I first tried this, I wrote a simple loop to check all divisors of a number and add them up.
# Program to check if a number is perfect using loops
num = 28 # You can change this number
divisor_sum = 0
# Loop through numbers less than num
for i in range(1, num):
if num % i == 0:
divisor_sum += i
if divisor_sum == num:
print(f"{num} is a Perfect Number")
else:
print(f"{num} is NOT a Perfect Number")You can see the output in the screenshot below.
If you run this with num = 28, you’ll see that it prints: 28 is a Perfect Number.
Method 2 – Program to Find a Perfect Number Using a Function
Since I often reuse this logic, I wrote it as a function. This way, I can check multiple numbers quickly.
# Function to check perfect number
def is_perfect(num):
divisor_sum = 0
for i in range(1, num):
if num % i == 0:
divisor_sum += i
return divisor_sum == num
# Test with a few numbers
for n in [6, 28, 12, 496]:
if is_perfect(n):
print(f"{n} is a Perfect Number")
else:
print(f"{n} is NOT a Perfect Number")Output:
6 is a Perfect Number
28 is a Perfect Number
12 is NOT a Perfect Number
496 is a Perfect NumberYou can see the output in the screenshot below.
This method is cleaner and reusable.
Method 3 – Program to Find a Perfect Number Using Recursion
Sometimes, I like experimenting with recursion. Here’s how I rewrote the same logic in a recursive style.
# Recursive function to check perfect number
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)
def is_perfect(num):
return sum_of_divisors(num) == num
# Example
num = 28
if is_perfect(num):
print(f"{num} is a Perfect Number")
else:
print(f"{num} is NOT a Perfect Number")You can see the output in the screenshot below.
Running this num = 28 gives 28 is a Perfect Number.
Check Perfect Numbers in a Range
In real projects, I often need to check more than one number. For example, let’s say I want all perfect numbers between 1 and 1000.
Here’s how I did it:
# Find all perfect numbers in a range
def is_perfect(num):
divisor_sum = 0
for i in range(1, num):
if num % i == 0:
divisor_sum += i
return divisor_sum == num
# Check numbers from 1 to 1000
for n in range(1, 1001):
if is_perfect(n):
print(n)Output:
6
28
496These are the three perfect numbers under 1000.
Real-Life Example
I once used this logic in a small coding workshop for high school students in Texas. The students loved the concept of “perfect” numbers because it felt like a puzzle.
They even extended the logic to check for abundant and deficient numbers. That’s the beauty of Python: you can take a simple concept and expand it into a bigger project.
When I started, I didn’t realize how easy it would be to check for perfect numbers in Python.
The loop method is simple, the function method is reusable, and the recursion method is just fun to experiment with.
If you’re practicing Python, try all three methods. You’ll not only learn about perfect numbers but also improve your problem-solving skills.
You may also read:
- Use the wait() Function in Python
- Use the find() Function in Python
- Use Exponential Functions in Python
- Use Counter Function in Python
I am Bijay Kumar, a Microsoft MVP in SharePoint. Apart from SharePoint, I started working on Python, Machine learning, and artificial intelligence for the last 5 years. During this time I got expertise in various Python libraries also like Tkinter, Pandas, NumPy, Turtle, Django, Matplotlib, Tensorflow, Scipy, Scikit-Learn, etc… for various clients in the United States, Canada, the United Kingdom, Australia, New Zealand, etc. Check out my profile.
