4 different Python programs to check if a number is a perfect number

Python program to check if a number is a perfect number or not:

In this post, we will learn how to check if a number is a perfect number or not in Python. I will show you different ways to write this program in Python. The program will take one number as input from the user and print a message if it is a perfect number or not.

But, before I start to write the program, let me quickly show you what is a perfect number and the algorithm to check for perfect numbers.

What is a perfect number:

A number is called a perfect number if the sum of the divisors of the number is equal to the number itself. For example, 28 is a perfect number, because the sum of its divisors 1, 2, 4, 7, 14 is equal to 28.

1 + 2 + 4 + 7 + 14 = 28

So, we have to find all the divisors of a number, find the sum of all divisors and compare it with the original number to check if a number is a perfect number or not.

Algorithm to check if a number is a perfect number or not:

We can use the below algorithm to check for a perfect number:

Take the number as input from the user and store it in a variable.
Initialize one variable as 0 to hold the sum of its divisors.
Run one loop from 1 to number - 1 and for each value of the loop, check if it is a divisor of the number or not.
- If it is a divisor, add it to the sum variable.
Once the loop ends, compare the sum variable with the original number. If both are equal, it will be a perfect number. Else, not.

We can also run the loop from 1 to number/2 as no value greater than number/2 can divide the number. It will reduce the loop iterations.

Method 1: Python program to check for a perfect number:

The below python program checks if a number is a perfect number or not:

no = int(input("Enter the number: "))
sum = 0

for i in range(1, no):
    if no % i == 0:
        sum += i

if sum == no:
    print(f'{no} is a perfect number.')
else:
    print(f'{no} is not a perfect number.')

Here,

The program asks the user to enter a number. It assigns the number to the no variable.
The sum variable is used to hold the sum of all divisors. It is initialized as 0.
The for loop runs from i = 1 to i = no. On each iteration of the loop, it checks if i can divide no or not. If yes, it adds its value to the sum variable.
Once the for loop ends, it compares the values of sum and no. If both are equal, it will be a perfect number.

If you run this program, it will print output as below:

Enter the number: 496
496 is a perfect number.

Enter the number: 8128
8128 is a perfect number.

Enter the number: 8129
8129 is not a perfect number.

Method 2: By iterating from 1 to number/2:

We can also iterate from 1 to number/2. As I explained above, it will reduce the number of steps of the loop.

Let me change the above program:

no = int(input("Enter the number: "))
sum = 0

for i in range(1, int(no/2)+1):
    if no % i == 0:
        sum += i

if sum == no:
    print(f'{no} is a perfect number.')
else:
    print(f'{no} is not a perfect number.')

Since the type of no/2 is float, we have to cast it to an integer. It will run from i = 1 to i = no/2.

If you run this program, it will print similar result.

Enter the number: 8128
8128 is a perfect number.

Method 3: By using while loops:

We can also use a while loop to write the same program. It will run from number/2 to 1 and find out the sum of all divisors.

no = int(input("Enter the number: "))
sum = 0
i = int(no/2)

while i > 0:
    if no % i == 0:
        sum += i
    i = i - 1

if sum == no:
    print(f'{no} is a perfect number.')
else:
    print(f'{no} is not a perfect number.')

We initialized a variable i as no/2. The while loop starts at i = no/2.
On each iteration of the loop, it checks if the number is divisible by the current value of i or not. If yes, it adds that value to the sum variable.
At the end of each iteration, it decrements the value of i by 1.
This loop stops when the value of i becomes 0.
It compares the values of sum and no once the loop ends to find if the given number is a perfect number or not.

It will give similar output.

Enter the number: 488
488 is not a perfect number.

Enter the number: 496
496 is a perfect number.

Method 4: By using a separate method:

Let’s use a separate method to write the above program. This method will take one number as its parameter and return one boolean value. It will return True if the number is a perfect number and False if it is not. Based on this value, the program will print if the given number is a perfect number or not.

def is_perfect(n):
    sum = 0

    for i in range(1, int(n/2)+1):
        if n % i == 0:
            sum += i
    return sum == n


no = int(input("Enter the number: "))
if is_perfect(no):
    print(f'{no} is a perfect number.')
else:
    print(f'{no} is not a perfect number.')