Prime Divisors - Python Programming Exercise

This Python program prompts the user to enter a number and then displays that number as a product of its prime factors. The program uses a factorization approach to find the prime factors of the entered number. It repeatedly divides the number by the smallest possible prime factor until the number becomes 1, accumulating the prime factors along the way. The result is displayed as a multiplication of the prime factors, showing the decomposition of the original number. This exercise highlights the use of loops, conditional statements, and integer arithmetic in Python. It also introduces the concept of prime factorization, an essential topic in number theory, and demonstrates how to break down a number into its prime components. By including a final factor of 1 in the output, the program ensures the format remains consistent and easy to understand, making it an excellent practice for working with mathematical operations and output formatting in Python.

 Category

Python Data Types

 Exercise

Prime Divisors

 Objective

Develop a Python program that displays a number (entered by the user) as a product of its prime factors. For example, 60 = 2 · 2 · 3 · 5

(Hint: it can be easier if the solution is displayed as 60 = 2 · 2 · 3 · 5 · 1)

 Example Python Exercise

 Copy Python Code 
# Prompt the user for a number
number = int(input("Enter a number: "))

# Initialize an empty list to store the prime factors
prime_factors = []

# Start with the smallest prime factor (2)
divisor = 2

# Loop to find prime factors
while number > 1:
    while number % divisor == 0:  # Check if the divisor is a factor
        prime_factors.append(divisor)  # Add the divisor to the list
        number //= divisor  # Divide the number by the divisor
    divisor += 1  # Move to the next possible divisor

# Display the result as a product of prime factors
print(f"The prime factors of the number are: {' * '.join(map(str, prime_factors))}")

 Output

Case 1:
Enter a number: 60
The prime factors of the number are: 2 * 2 * 3 * 5

Case 2:
Enter a number: 100
The prime factors of the number are: 2 * 2 * 5 * 5

Case 3:
Enter a number: 7
The prime factors of the number are: 7

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