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Easy2Siksha
(b) Write a program to calculate the factorial of a number using recursion
Ans: A Fun Journey Into Factorial Land
Imagine you're going on a little adventure to a magical land where numbers behave in
interesting ways. Today, we’re going to visit Factorial Land, where numbers love to multiply
and grow bigger and bigger in a unique way. In this magical land, there’s a fascinating rule:
Every number loves to grow by multiplying itself with all the numbers before it! Let's take a
walk through this fun journey and learn how to calculate the factorial of a number using a
magic trick called recursion.
What is a Factorial?
To start, let’s break down the rule of factorials. If you're in Factorial Land and you meet a
number, let's say 5, it will tell you its factorial. The factorial of 5 is simply 5 × 4 × 3 × 2 × 1.
It’s as if the number is multiplying itself with all the numbers before it until it reaches 1.
For example:
• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 4! = 4 × 3 × 2 × 1 = 24
• 3! = 3 × 2 × 1 = 6
• 2! = 2 × 1 = 2
• 1! = 1 (1 is special; it stays as 1)
And guess what? There’s even a rule for 0!. You might be wondering, "What’s the factorial
of 0?" Well, in Factorial Land, they say that 0! = 1, which is a little surprise but is the way it
works in mathematics.
Why Use Recursion?
Now that we know what a factorial is, let’s talk about how we can calculate it using
recursion. Recursion is like a magical mirror that can reflect itself back! It’s like when you
look into a mirror and you see another mirror reflecting your image over and over again, but
with a twist. In programming, recursion happens when a function calls itself to solve smaller
pieces of a problem until it reaches a simple base case.
Think about it like this:
• If you want to calculate the factorial of a number, say 5, you can think of it like this:
“What is the factorial of 5?”
• You can break it down into: “What is the factorial of 4?” (And you keep asking
smaller questions until you get down to 1, which is simple and known).
Once we reach that base case (which is the smallest possible problem), we can start putting
everything together, just like solving a puzzle!