Python Program to Find All the Divisors of an Integer

1. Introduction

In this tutorial, we will learn how to write a Python program to find all the divisors of an integer.

The task of finding all divisors of an integer is a common problem in programming and mathematics. This operation is essential for algorithms related to number theory, such as finding prime numbers or factoring composite numbers. Python can handle this task efficiently using simple loops and conditional statements.

A divisor of an integer is any number that divides it without leaving a remainder. In other words, if the result of dividing the integer by some number is an integer, then that number is considered a divisor of the original integer.

2. Program Steps

1. Define an integer to find the divisors of.

2. Loop through all possible divisors from 1 to the integer itself.

3. Check if the current number is a divisor by using the modulus operator.

4. If the modulus is zero, it means the current number is a divisor, so print or store it.

5. Continue the process until all possible divisors have been checked.

3. Code Program

# Function to print the divisors of an integer
def print_divisors(n):
    # Start with 1 and check up to n
    for i in range(1, n + 1):
        # If i is a divisor of n, print it
        if n % i == 0:
            print(i)

# Number to find divisors of
number = 28
# Call the function and print the divisors
print_divisors(number)

Output:

1
2
4
7
14
28

Explanation:

1. The function print_divisors is defined to take an integer n as its argument.

2. A for loop iterates through all numbers from 1 to n inclusive, using i as the loop variable.

3. In each iteration, the function checks if n % i == 0, which uses the modulus operator to determine if i is a divisor of n.

4. If the condition is True, i is printed, as it is a divisor.

5. This process continues until all numbers from 1 to n have been checked.

6. When the function is called with number (28), it prints out all divisors of 28, which are 1, 2, 4, 7, 14, and 28.