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# Python Program to Find Product of Two Numbers using Recursion

This Python program calculates the product of two numbers using recursion.

Recursion is a powerful programming technique where a function calls itself to solve a smaller instance of the same problem. It allows for elegant and concise solutions to certain types of problems. In Python, you can implement recursion by defining a function that calls itself within its body.

## Program Statement

Write a Python program that calculates the product of two numbers using recursion. The program should prompt the user to enter two numbers and then use a recursive function to find their product. The program should display the result to the user.

The program should adhere to the following specifications:

1. Define a function `multiply_recursive(a, b)` that takes two numbers `a` and `b` as parameters.
2. Implement the `multiply_recursive` function using recursion to find the product of `a` and `b`.
3. Handle the base case: if either `a` or `b` is 0, the product should be 0.
4. In the recursive case, multiply `a` by `(b - 1)` and add `a` to the result. This is equivalent to the formula `a * b = a + a * (b - 1)`.
5. Prompt the user to enter the first number (`num1`) and the second number (`num2`).
6. Call the `multiply_recursive` function with `num1` and `num2` as arguments to calculate their product.
7. Display the product of the two numbers to the user.

Ensure that the program is able to handle positive integers, zero, and negative integers as input.

## Python Program to Find Product of Two Numbers using Recursion

```def multiply_recursive(a, b):
# Base case: if either number is 0, the product is 0
if a == 0 or b == 0:
return 0

# Recursive case: multiply a by b-1 and add a to the result
# This is equivalent to a * b = a + a * (b - 1)
return a + multiply_recursive(a, b - 1)

# Test the function
num1 = 4
num2 = 5
product = multiply_recursive(num1, num2)
print(f"The product of {num1} and {num2} is: {product}")
```

## How it works

1. The program starts by defining a recursive function `multiply_recursive(a, b)`. This function takes two parameters `a` and `b`, representing the two numbers for which we want to calculate the product.
2. Inside the `multiply_recursive` function, we have a base case that checks if either `a` or `b` is 0. If either number is 0, the product is also 0, so we return 0.
3. In the recursive case, we multiply `a` by `(b - 1)` and add `a` to the result. This step corresponds to the formula `a * b = a + a * (b - 1)`. By recursively calling `multiply_recursive(a, b - 1)`, we break down the problem into smaller subproblems until we reach the base case.
4. The program prompts the user to enter the first number (`num1`) and the second number (`num2`) using the `input()` function. The `int()` function is used to convert the input strings to integers.
5. The `multiply_recursive` function is then called with `num1` and `num2` as arguments, and the result is assigned to the variable `product`.
6. Finally, the program displays the product of the two numbers using `print()`, along with a formatted string that includes the input numbers and the calculated product.

When you run the program, it follows these steps to calculate the product of the two numbers using recursion. The recursion occurs as the function repeatedly calls itself with smaller values of `b` until it reaches the base case. Once the base case is reached, the recursive calls start returning their values, and the product is calculated.

## Input/Output

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