Python: Find the largest integer divisor of a number n that is less than n

Last update on May 28 2022 13:41:20 (UTC/GMT +8 hours)

Python Programming Puzzles: Exercise-37 with Solution

A divisor is a number that divides another number either completely or with a remainder.

Write a Python program to find the largest integer divisor of a number n that is less than n.

Input: 
18
Output:
9
Input: 
100
Output:
50
Input: 
102
Output:
51
Input: 
500
Output:
250
Input: 
1000
Output:
500
Input: 
6500
Output:
3250

Pictorial Presentation:

Python: Find the largest integer divisor of a number n that is less than n.

Sample Solution:

Python Code:

#License: https://bit.ly/3oLErEI

def test(n):
     return next(d for d in range(n - 1, 0, -1) if n % d == 0)
 
n = 18
print("Original number:",n)
print("Largest integer divisor of a number n that is less than n:")
print(test(n))
n = 100
print("Original number:",n)
print("Largest integer divisor of a number n that is less than n:")
print(test(n))
n = 102
print("Original number:",n)
print("Largest integer divisor of a number n that is less than n:")
print(test(n))
n = 500
print("Original number:",n)
print("Largest integer divisor of a number n that is less than n:")
print(test(n))
n = 1000
print("Original number:",n)
print("Largest integer divisor of a number n that is less than n:")
print(test(n))
n = 6500
print("Original number:",n)
print("Largest integer divisor of a number n that is less than n:")
print(test(n))

Sample Output:

Original number: 18
Largest integer divisor of a number n that is less than n:
9
Original number: 100
Largest integer divisor of a number n that is less than n:
50
Original number: 102
Largest integer divisor of a number n that is less than n:
51
Original number: 500
Largest integer divisor of a number n that is less than n:
250
Original number: 1000
Largest integer divisor of a number n that is less than n:
500
Original number: 6500
Largest integer divisor of a number n that is less than n:
3250

Flowchart:

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

Python Code Editor :

Have another way to solve this solution? Contribute your code (and comments) through Disqus.

Previous: Find the largest k numbers.
Next: Sort the numbers by the sum of their digits.

Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

The os and os.path modules.

The __file__ constant

os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")

os.path.dirname(path) (returns "the directory name of pathname path")

os.getcwd() (returns "a string representing the current working directory")

os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m