Overview

In this post I’ll create a function in Python that can quickly find the largest integer divisor in common between two whole numbers. For example, if I pass the function a value of 100 and 150, then the function would find the largest common divisor to be 50 (100/50 = 2, 150/50 = 3). No larger number can divide evenly into 100 and 150.

Code Explanation

def largest_divisor_finder(value1, value2):
    # find which value is smaller
    value1 = 48
    value2 = 72

    smaller = min(value1, value2)
    
    # divisor range to be checked
    divisors = set(range(2, smaller+1))

    # all whole numbers are divisible by at least 1
    answer = 1
    
    # iterate until list is empty
    while divisors:
        test_divisor = divisors.pop()
        if value1 % test_divisor == 0 and value2 % test_divisor == 0:
            answer = test_divisor
        else:
            multiples_to_remove = set(range(test_divisor*2, smaller + 1, test_divisor))
            divisors.difference_update(multiples_to_remove)

    print(f"The largest integer divisor of the whole numbers {value1} and {value2} is {answer}.")

Name the Function

First I name the function largest_divisor_finder, and have that function take two arguments: value1 and value2. value1 and value2 are the two whole numbers which the user desires to find a common divisor for.

def largest_divisor_finder(value1, value2):

Example Calculation

For an example, I will set value1 to 48 and value2 to 72. In this example I will find the largest number that divides evenly into both numbers.

value1 = 48
value2 = 72

largest_divisor_finder(value1, value2)

Numbers to Search for Common Divisors

Next I create a set of all the numbers I want to search through in order to find the largest common divisor. The smallest number (other than 1) that could potentially divide into both numbers is 2, so I begin the set at 2. Then I include each whole number from 2 to the smaller of value1 and value2 using the range function. I write smaller+1 as the range function is not inclusive of the ending number.

smaller = min(value1, value2)
    
# divisor range to be checked
divisors = set(range(2, smaller+1))

print(divisors)
>>> {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Loop through the Divisors Set

Next I create a while loop to find common divisors. The while loop runs as long as there are numbers to check in the divisors set. In order to make sure this loop doesn’t run forever, I will remove numbers from divisors during each pass through the loop.

# iterate until list is empty
while divisors:

Find and Test the Next Number from the Divisors Set

The first action inside the loop is to remove the lowest number (2) from divisors. I set the variable test_divisor equal to this number (2).

test_divisor = divisors.pop()

print(test_divisor)
>>> 2
print(divisors)
>>> {3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48}

Next I test to see if test_divisor divides evenly into value1 and value2. If so, then I update the answer to be test_advisor.

if value1 % test_divisor == 0 and value2 % test_divisor == 0:
    answer = test_divisor

print(answer)
>>> 2

If not, then I remove all multiples of the test_divisor from the divisors set. This will shorten the number of times that the while loop executes. In this example, this first happens when the test_divisor is 5. Any number divisible by 5 is removed from the divisor set.

else:
    multiples_to_remove = set(range(test_divisor*2, smaller + 1, test_divisor))
    divisors.difference_update(multiples_to_remove)
print(multiples_to_remove)
>>> {10,15,20,25,30,35,40,45}
print(divisors)
>>> {6,7,8,9,11,12,13,14,16,17,18,19,21,22,23,24,26,27,28,29,31,32,33,34,36,37,38,39,41,42,43,44,46,47,48}

Finish the Loop

I continue executing the loop until there are no more numbers to check in the divisors set. At this point, my answer will be the following:

print(answer)
>>> 24

Display the Results

Finally I print the findings: the largest integer that divides evenly into both 48 and 72.

print(f"The largest integer divisor of the whole numbers {value1} and {value2} is {answer}.")
>>> The largest integer divisor of the whole numbers 48 and 72 is 24.

Now I can pass any 2 positive integers to the function and watch the function do the heavy lifting.

As an example I will pass the large numbers: 128,245 and 134,509,830.

largest_divisor_finder(value1=128245, value2=134509830)
>>> The largest integer divisor of the whole numbers 128245 and 134509830 is 65.

In a few short lines of code I created a tool for finding the largest integer divisor of two whole numbers that operates with speed and accuracy.