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:

- Prompt the user to enter a positive integer.
- 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.
- Define a function called
`prime_factors(n)`

that takes the input number`n`

as a parameter. - Initialize an empty list called
`factors`

to store the prime factors. - Initialize a variable
`i`

to 2. - 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`

. - 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. - If
`n`

is not divisible by`i`

, increment`i`

by 1 and continue to the next iteration of the loop. - 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. - Return the
`factors`

list. - Call the
`prime_factors()`

function with the input number and store the result in a variable. - 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.