- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Count digits in a factorial in C++

We are given an integer value and the task is to first calculate the factorial of a number and then calculate the total number of digits in a result.

## What is a factorial number

Factorial of a number is calculated by multiplying the digits in a number while decrementing the value of digit by 1. It is denoted by the symbol ‘!’ i.e. 0!, 1!, 2!, 3!, 5!,....,etc. Factorial of 0! and 1! is always 1.

I.e. factorial of 2 = 2 * (2-1) = 2 * 1 = 2 factorial of 3 = 3 * (3-1) * (2-1) = 3 * 2 * 1 = 6

## For Example

Input− factorial(6)Output− number of digits in factorial(6) is: 3

**Explanation** − since the factorial value of 6 is 720 and it contains 3 digits therefore, the result is 3

Input− factorial(12)Output− number of digits in factorial(12) is: 9

**Explanation** − since the factorial value of 12 is 479001600 and it contains 9 digits therefore, the result is 9.

## Approach used in the below program is as follows

Input the number of which factorial needs to be calculated .

If the number is less than 0 then return 0 because negative number don’t have any factorial value

If the number is 1 then return 1 because 1! Is 1 and it has 1 digit.

If the number is greater than 1 i.e. starts with 2 or more than create one loop, starting from 2 till it is less than or equals to number

Take one temporary variable let’s say d and initialise it with 0 outside the loop and inside the loop keep adding it with the value of log10(i) till every iteration of i.

After that, return the floor value of ‘floor(d)+1’

Print the result.

## Example

#include <iostream> #include <cmath> using namespace std; // This function returns the number of digits present in num! int count_digits(int num){ // factorial exists only if num <= 0 if (num < 0){ return 0; } // base case if (num <= 1){ return 1; } // else iterate through num and calculate the // value double d = 0; for (int i=2; i<=num; i++){ d += log10(i); } return floor(d) + 1; } int main(){ cout<<"number of digits in factorial(1) is: "<<count_digits(1)<< endl; cout<<"number of digits in factorial(6) is: "<<count_digits(6) << endl; cout<<"number of digits in factorial(106) is: "<<count_digits(106) << endl; return 0; }

## Output

If we run the above code it will generate the following output −

number of digits in factorial(1) is: 1 number of digits in factorial(6) is: 3 number of digits in factorial(106) is: 171

- Related Questions & Answers
- Count factorial numbers in a given range in C++
- Find sum of digits in factorial of a number in C++
- Count trailing zeros in factorial of a number in C++
- C/C++ Program to Count trailing zeroes in factorial of a number?
- C/C++ Programming to Count trailing zeroes in factorial of a number?
- Returning number of digits in factorial of a number in JavaScript
- Count Numbers with Unique Digits in C++
- C# factorial
- Calculating the sum of digits of factorial JavaScript
- Count ways to spell a number with repeated digits in C++
- Python – Average digits count in a List
- Python Program to Count trailing zeroes in factorial of a number
- Java Program to Count trailing zeroes in factorial of a number
- Count even and odd digits in an Integer in C++
- Count number of digits after decimal on dividing a number in C++