## 1. Overview

In this tutorial, **we’ll discuss an efficient approach to find the sum of digits in the factorial of a number.** We’ll also present an algorithm and discuss the steps in detail.

## 2. Problem Statement

**Given a number , we need to find the factorial of the number and then add the digits in the factorial.**

Let’s take an example to understand the problem and the expected output. We’re taking a random number . So here . The first step is to calculate the factorial of .

The general formula for calculating the factorial of a number is . Now here :

The final step is to add the digits in the factorial. For this example, the final result would be:

## 3. Our Approach

Given a number , **we’ll calculate factorial using the previous formula.** **Next, we’ll take the factorial and find the last digit of the factorial.** As soon as we find the last digit of the factorial, we’ll store it in a temporary variable (e.g., ) and remove the last digit from the factorial. We’ll repeat this process and continue adding the digits:

## 4. Pseudocode

Now let’s see the pseudocode:

```
algorithm SumFactorial(N):
// INPUT
// N = a positive integer number
// OUTPUT
// Sum of digits in the factorial of N
factorial <- 1
result <- 0
for k <- 1 to N:
factorial <- factorial * k
while factorial != 0:
last_digit <- factorial mod 10
result <- result + last_digit
factorial <- factorial / 10
return result
```

Here we’re taking an integer number as an input. We use a variable to store the factorial of the input . The variable stores the last digits of the factorial. Finally, we’re adding the digits in the factorial of in the variable .

Now to remove the last digit from the at every iteration, we divide it with and reassign the quotient in .

## 5. Conclusion

In this tutorial, we showed how to find the sum of digits of a factorial. We discussed our approach and presented an algorithm to achieve the solution to the given problem.