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

Last update on April 17 2025 13:03:00 (UTC/GMT +8 hours)

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

Largest Proper Divisor

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

Visual 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

# Define a function named 'test' that takes an integer 'n' as input
def test(n):
    # Return the largest integer divisor of 'n' that is less than 'n'
    return next(d for d in range(n - 1, 0, -1) if n % d == 0)

# Assign a specific value 'n' to the variable
n = 18

# Print a message indicating the original number
print("Original number:", n)

# Print a message indicating the operation to be performed
print("Largest integer divisor of a number n that is less than n:")
# Print the result of the test function applied to 'n'
print(test(n))

# Assign another specific value 'n' to the variable
n = 100

# Print a message indicating the original number
print("\nOriginal number:", n)

# Print a message indicating the operation to be performed
print("Largest integer divisor of a number n that is less than n:")
# Print the result of the test function applied to 'n'
print(test(n))

# Assign another specific value 'n' to the variable
n = 102

# Print a message indicating the original number
print("\nOriginal number:", n)

# Print a message indicating the operation to be performed
print("Largest integer divisor of a number n that is less than n:")
# Print the result of the test function applied to 'n'
print(test(n))

# Assign another specific value 'n' to the variable
n = 500

# Print a message indicating the original number
print("\nOriginal number:", n)

# Print a message indicating the operation to be performed
print("Largest integer divisor of a number n that is less than n:")
# Print the result of the test function applied to 'n'
print(test(n))

# Assign another specific value 'n' to the variable
n = 1000

# Print a message indicating the original number
print("\nOriginal number:", n)

# Print a message indicating the operation to be performed
print("Largest integer divisor of a number n that is less than n:")
# Print the result of the test function applied to 'n'
print(test(n))

# Assign another specific value 'n' to the variable
n = 6500

# Print a message indicating the original number
print("\nOriginal number:", n)

# Print a message indicating the operation to be performed
print("Largest integer divisor of a number n that is less than n:")
# Print the result of the test function applied to '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:

For more Practice: Solve these Related Problems:

Write a Python program to find the largest divisor of a given number that is less than the number itself using iteration.
Write a Python program to determine the proper divisors of a number and select the maximum among them.
Write a Python program to use a for-loop to test potential divisors from n//2 downwards and return the first divisor found.
Write a Python program to compute the largest proper divisor by iterating from 1 to n-1 and checking divisibility.

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Python Code Editor :

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