Recursion is a way to solve larger problems by dividing them into smaller problems. In other words, recursion is breaking the big problem into smaller similar problems to solve them and get the actual results. Often, recursion is termed as a function calling itself. It might sound strange, but the fact is the function must call itself when it is in recursion. What does this look like? Let's look at an example,

In mathematics, the term "factorial" is very popular. A factorial of a number N is defined as multiplication of all positive integers less than and equal to N. It is always denoted with ! (an exclamation mark). So, a factorial of 5 can be written as follows:

5! = 5 X 4 X 3 X 2 X 1

Similarly, we can write the following factorials of the given number::

4! = 4 X 3 X 2 X 1

3! = 3 X 2 X 1

2! = 2 X 1

1! = 1

If we look closely at our example, we can see that we can write factorial of 5 in terms of factorials of 4 like this:

5! = 5 X 4!

Similarly, we can write:

4! = 4 X 3!

3! = 3 X 2!

2! = 2 X 1!

1! = 1 X 0!

0! = 1

Alternatively, we can simply say in general terms that:

n! = n * (n-1)!

This represents recursion. We are breaking each of the steps into smaller ones and solving the actual big problem. Here is an image to show how a factorial of 3 is calculated:

So, the steps are as follows:

1. 3! = 3 X 2!
2. 2! = 2 X 1!
3. 1! = 1 X 0!
4. 0! = 1
5. 1! = 1 X 1 = 1
6. 2! = 2 X 1 = 2
7. 3! = 3 X 2 = 6