Python Program to Find the Prime Factors of a Number

The provided Python program is designed to find the prime factors of a given number. It utilizes a function called prime_factors() to accomplish this task. The program takes a number as input, either from the user or as a command-line argument, and proceeds to calculate the prime factors.

Problem Statement

Write a Python program that prompts the user to enter a positive integer and then finds and displays the prime factors of that number.

Requirements:

• The program should validate that the input is a positive integer. If the input is invalid, display an error message and prompt the user again until a valid input is provided.
• The program should calculate and display all the prime factors of the given number.
• The prime factors should be displayed in ascending order.

Python Program to Find the Prime Factors of a Number

def prime_factors(n):
    factors = []
    i = 2

    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)

    if n > 1:
        factors.append(n)

    return factors

# Example usage
number = int(input("Enter a number: "))
factors = prime_factors(number)

print("Prime factors of", number, "are:", factors)

How it Work

The Python program to find the prime factors of a given number works as follows:

1. Prompt the user to enter a positive integer.
2. Validate the input to ensure it is a positive integer. If the input is invalid (not a positive integer), display an error message and prompt the user again until a valid input is provided.
3. Define a function called prime_factors(n) that takes the input number n as a parameter.
4. Initialize an empty list called factors to store the prime factors.
5. Initialize a variable i to 2.
6. Use a while loop that runs until i * i is greater than n. This optimization ensures that we only check potential factors up to the square root of n.
7. Inside the while loop, check if n is divisible evenly by i. If it is, divide n by i, append i to the factors list, and continue to the next iteration of the loop.
8. If n is not divisible by i, increment i by 1 and continue to the next iteration of the loop.
9. After the while loop, check if n is greater than 1. If it is, it means n itself is a prime number, so append it to the factors list.
10. Return the factors list.
11. Call the prime_factors() function with the input number and store the result in a variable.
12. Print the prime factors of the given number.

The program follows this algorithm to find the prime factors of the input number. It utilizes a while loop, division, and iteration to determine the prime factors. The output is then displayed to the user.

Input/ Output

Explanation: The user enters the number 56. The prime factors of 56 are 2, 2, 2, and 7. The program calculates and displays the prime factors in ascending order.