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# How to determine if a number is a perfect number in python

Sai Venkatesh Raju

A number is a perfect number if the sum of its factors (excluding itself) is equal to the number.

## Example

1. Consider 63
Factors of 63, excluding itself, are: 1, 3, 7, 9, and 21
The sum of its factors are: 1 + 3 + 7 + 9 + 21 = 41
So, 63 is not a perfect number.

2. Consider 6
Factors of 6, excluding itself, are: 1, 2, and 3
The sum of its factors are: 1 + 2 + 3 = 6
So, 6 is a perfect number.\

Fun fact: 6 is the first perfect number in the set of Natural numbersnatural numbers are whole even numbers.

So, now we understand what a perfect number is and how to determine if a given number is a perfect number.
Let’s write a program capturing our approach.
Points to consider:

1. Boundaries:
We need to compute the sum of all factors (excluding itself) of given number – this means that iterationfor/while/do…while is involved. The number itself must not be part of the sum; so, let’s start at $1$ and go down to $1$ as that is the least possible factor that a non-negative integer could have.
2. Differentiate between wanted and unwanted entities:
Here, the wanted entities are the factors of the given number. We can utilize the mod operator to differentiate between factors and non-factors.
3. Tracking:
We will keep track of the sumthe sum is set to 0 before the loop starts of factors. Once the loop is complete, we will compare the sum with the number to figure out whether our number is perfect or non-perfect.
# Function to determine if given number is a perfect number
# Input: Number (Range: [1, sys.maxsize])
# Output: A string detailing if given number is perfect or not
def Perfect_Number(num):
count=num-1             # count will be our iterator and facilitate our exit from the loop when needed (i.e. when its value = 0)
sum=0                   # our tracking variable sum
while count!=0:
if num%count == 0:    # when num is divisible by count with 0 as remainder, it means count is a factor of num
sum += count        # adding factor to the sum
count-=1              # decrementing count to explore the next number
if sum == num:          # Comparing sum with num, to get the verdict of perfect/non-perfect number
print(num,"is a perfect number")
else:
print(num,"is not a perfect number")

#Invoking the function
#PerfectNumbers
Perfect_Number(6)         # Calling the function and giving 6 as input to check whether it is a perfect number or not
Perfect_Number(28)

#Not a perfect number
Perfect_Number(63)

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Sai Venkatesh Raju
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