Question

A proper divisor of a positive integer, n, is a positive integer less than n which divides evenly into n. Write a function that computes all of the proper divisors of a positive integer. The integer will be passed to the function as its only parameter. The function will return a list containing all of the proper divisors as its only result. Complete this exercise by writing a main program that demonstrates the function by reading a value from the user and displaying the list of its proper divisors. Ensure that your main program only runs when your solution has not been imported into another file.

Answer 1

A function named find_proper_divisors calculates all proper divisors of a positive integer by checking each number less than the integer for even division. The main program demonstrates the function's use by reading a user's input and displaying the found divisors. This example is written in Python and entails iteration and modulo operations.

Step-by-step explanation:

To find all the proper divisors of a positive integer n, one can divide n by each of the integers less than n and determine which ones result in an even division without a remainder. This concept of finding divisors connects to division in mathematics where, unlike multiplication, the exponents do not need to match for division to be carried out. Below is a Python function that accomplishes this task along with a main program that uses the function.

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

if __name__ == '__main__':
value = int(input('Enter a positive integer: '))
divisors = find_proper_divisors(value)
print('The proper divisors of', value, 'are:', divisors)

The function find_proper_divisors iterates through all integers from 1 up to but not including n, checks if n is divisible by the integer, and if so, adds it to the list of proper divisors. The main program reads an integer from the user, calls the function, and then prints the list of divisors. Remember, this code will only execute its main section if it's not imported as a module elsewhere.