How to Check if a Number is Divisible by Another Number in Python

Determining if one number can be evenly divided by another is a fundamental arithmetic operation used in various programming tasks, from data validation to mathematical algorithms like finding factors or checking for even/odd numbers.

Python provides a straightforward way to perform this check using the modulo operator.

This guide demonstrates how to check for divisibility in Python, handle multiple conditions, and filter lists based on divisibility.

The Modulo Operator (%) for Divisibility

The core tool for checking divisibility in Python is the modulo operator (%). This operator performs division but returns only the remainder of that division.

remainder1 = 10 % 3  # 10 divided by 3 is 3 with a remainder of 1
print(remainder1)    # Output: 1

remainder2 = 12 % 4  # 12 divided by 4 is 3 with a remainder of 0
print(remainder2)    # Output: 0

remainder3 = 15 % 4  # 15 divided by 4 is 3 with a remainder of 3
print(remainder3)    # Output: 3

The key insight for divisibility is: If a number A is perfectly divisible by another number B, the remainder of their division (A % B) will be exactly 0.

Checking if a Number IS Divisible by Another

To check if number_a is divisible by number_b, calculate number_a % number_b and see if the result is equal (==) to 0.

number_a = 16
number_b = 4

is_divisible = (number_a % number_b == 0)

print(f"Remainder of {number_a} % {number_b} is: {number_a % number_b}")

print(f"Is {number_a} divisible by {number_b}? {is_divisible}")

if number_a % number_b == 0:
    print(f"{number_a} is perfectly divisible by {number_b}.")
else:
    print(f"{number_a} is NOT perfectly divisible by {number_b}.")

Output:

Remainder of 16 % 4 is: 0
Is 16 divisible by 4? True
16 is perfectly divisible by 4.

Checking if a Number is NOT Divisible by Another

To check if number_a is not divisible by number_b, calculate number_a % number_b and see if the result is not equal (!=) to 0.

number_a = 17
number_b = 4

is_not_divisible = (number_a % number_b != 0)

print(f"Remainder of {number_a} % {number_b} is: {number_a % number_b}")

print(f"Is {number_a} NOT divisible by {number_b}? {is_not_divisible}")

if number_a % number_b != 0:
    print(f"{number_a} is NOT perfectly divisible by {number_b}.")
else:
    print(f"{number_a} is perfectly divisible by {number_b}.")

Output:

Remainder of 17 % 4 is: 1
Is 17 NOT divisible by 4? True
17 is NOT perfectly divisible by 4.

Filtering Lists for Divisible Numbers

You can easily extract numbers from a list that are divisible by a specific divisor.

Using List Comprehension

List comprehensions provide a concise way to create a new list based on an existing one, filtering elements based on a condition.

numbers = [10, 15, 20, 25, 30, 35, 40]
divisor = 5

divisible_by_5 = [num for num in numbers if num % divisor == 0]

print(f"Original list: {numbers}")

print(f"Numbers divisible by {divisor}: {divisible_by_5}")

divisible_by_10 = [num for num in numbers if num % 10 == 0]
print(f"Numbers divisible by 10: {divisible_by_10}")

Output:

Original list: [10, 15, 20, 25, 30, 35, 40]
Numbers divisible by 5: [10, 15, 20, 25, 30, 35, 40]
Numbers divisible by 10: [10, 20, 30, 40]

The expression num % divisor == 0 acts as the filter condition within the list comprehension.

Using the filter() Function

The built-in filter() function can achieve the same result, often used with a lambda function for the condition.

numbers = [10, 15, 20, 25, 30, 35, 40]
divisor = 10

filtered_iterator = filter(lambda x: x % divisor == 0, numbers)

divisible_by_10_filter = list(filtered_iterator)

print(f"Original list: {numbers}")
print(f"Numbers divisible by {divisor} (using filter): {divisible_by_10_filter}")

• lambda x: x % divisor == 0: An anonymous function that takes an element x and returns True if it's divisible by divisor, False otherwise.
• filter(...): Returns an iterator yielding only the elements for which the lambda function returned True.
• list(...): Converts the iterator into a list.

Handling User Input for Divisibility Checks*

When getting numbers from user input, remember that the input() function returns a string. You must convert these strings to integers using int() before performing arithmetic operations like modulo.

try:
    input_str_1 = input('Enter the dividend (number to be divided): ')
    num_1 = int(input_str_1)

    input_str_2 = input('Enter the divisor: ')
    num_2 = int(input_str_2)

    if num_2 == 0:
         print("Error: Can not divide by zero.")
    elif num_1 % num_2 == 0:
        print(f"{num_1} IS divisible by {num_2}")
    else:
        print(f"{num_1} is NOT divisible by {num_2}")

except ValueError:
    print("Invalid input. Please enter whole numbers only.")
except ZeroDivisionError: # Though checked explicitly above, good practice
    print("Error: Division by zero is not allowed.")

Checking Divisibility by Multiple Numbers (AND Condition)

To check if a number is divisible by two or more other numbers, use the logical and operator to combine multiple modulo checks. The overall condition is True only if all individual divisibility checks are True.

num = 30

if num % 2 == 0 and num % 3 == 0 and num % 5 == 0:
    print(f"{num} is divisible by 2, 3, and 5.")
else:
    print(f"{num} is NOT divisible by all of 2, 3, and 5.")

num = 20
if num % 2 == 0 and num % 3 == 0 and num % 5 == 0:
     print(f"{num} is divisible by 2, 3, and 5.")
else:
    print(f"{num} is NOT divisible by all of 2, 3, and 5.")

Checking Divisibility by One of Multiple Numbers (OR Condition)

To check if a number is divisible by at least one of several other numbers, use the logical or operator. The overall condition is True if any of the individual divisibility checks are True.

num = 21

if num % 5 == 0 or num % 7 == 0:
    print(f"{num} is divisible by 5 or 7 (or both).")
else:
    print(f"{num} is divisible by neither 5 nor 7.")

num = 12
if num % 5 == 0 or num % 7 == 0:
     print(f"{num} is divisible by 5 or 7 (or both).")
else:
    print(f"{num} is divisible by neither 5 nor 7.")

Conclusion

Checking for divisibility in Python is efficiently handled using the modulo operator (%).

• A remainder of 0 indicates that a number is perfectly divisible by another.
• You can combine this check with standard comparison operators (==, !=) and logical operators (and, or) to test various conditions.
• List comprehensions and the filter() function offer concise ways to select numbers from a list based on divisibility criteria.

Remember to convert user input to integers using int() and handle potential errors like non-numeric input or division by zero.