Skip to content
Related Articles

Related Articles

Table of Contents

Improve Article
Save Article
Like Article

Find sum of digits in factorial of a number

  • Difficulty Level : Medium
  • Last Updated : 27 Apr, 2021

Given a number n, write code to find the sum of digits in the factorial of the number. Given n ≤ 5000
 

Examples: 

Input : 10
Output : 27

Input : 100
Output : 648

It is not possible to store a number as large as 100! under some data types so, idea is to store an extremely large number in a vector. 
 

1) Create a vector to store factorial digits and
   initialize it with 1.
2) One by one multiply numbers from 1 to n to 
   the vector. We use school mathematics for this
   purpose.
3) Sum all the elements in vector and return the sum.

C++




// C++ program to find sum of digits in factorial
// of a number
#include <bits/stdc++.h>
using namespace std;
 
// Function to multiply x with large number
// stored in vector v. Result is stored in v.
void multiply(vector<int> &v, int x)
{
    int carry = 0, res;
    int size = v.size();
    for (int i = 0 ; i < size ; i++)
    {
        // Calculate res + prev carry
        int res = carry + v[i] * x;
 
        // updation at ith position
        v[i] = res % 10;
        carry = res / 10;
    }
    while (carry != 0)
    {
        v.push_back(carry % 10);
        carry /= 10;
    }
}
 
// Returns sum of digits in n!
int findSumOfDigits(int n)
{
    vector<int> v;     // create a vector of type int
    v.push_back(1);    // adds 1 to the end
 
    // One by one multiply i to current vector
    // and update the vector.
    for (int i=1; i<=n; i++)
        multiply(v, i);
 
    // Find sum of digits in vector v[]
    int sum = 0;
    int size = v.size();
    for (int i = 0 ; i < size ; i++)
        sum += v[i];
    return sum;
}
 
// Driver code
int main()
{
    int n = 1000;
    cout << findSumOfDigits(n);
    return 0;
}
Java



// Java program to find sum of digits in factorial
// of a number
import java.util.*;
class GFG{
// Function to multiply x with large number
// stored in vector v. Result is stored in v.
static ArrayList<Integer> v=new ArrayList<Integer>();
static void multiply(int x)
{
    int carry = 0;
    int size = v.size();
    for (int i = 0 ; i < size ; i++)
    {
        // Calculate res + prev carry
        int res = carry + v.get(i) * x;
 
        // updation at ith position
        v.set(i,res % 10);
        carry = res / 10;
    }
    while (carry != 0)
    {
        v.add(carry % 10);
        carry /= 10;
    }
}
 
// Returns sum of digits in n!
static int findSumOfDigits(int n)
{
    v.add(1); // adds 1 to the end
 
    // One by one multiply i to current vector
    // and update the vector.
    for (int i=1; i<=n; i++)
        multiply(i);
 
    // Find sum of digits in vector v[]
    int sum = 0;
    int size = v.size();
    for (int i = 0 ; i < size ; i++)
        sum += v.get(i);
    return sum;
}
 
// Driver code
public static void main(String[] args)
{
    int n = 1000;
    System.out.println(findSumOfDigits(n));
}
}
// this code is contributed by mits
Python 3



# Python 3 program to find sum of digits
# in factorial of a number
 
# Function to multiply x with large number
# stored in vector v. Result is stored in v.
def multiply(v, x):
    carry = 0
    size = len(v)
    for i in range(size):
         
        # Calculate res + prev carry
        res = carry + v[i] * x
 
        # updation at ith position
        v[i] = res % 10
        carry = res // 10
 
    while (carry != 0):
        v.append(carry % 10)
        carry //= 10
 
# Returns sum of digits in n!
def findSumOfDigits( n):
    v = []     # create a vector of type int
    v.append(1) # adds 1 to the end
 
    # One by one multiply i to current
    # vector and update the vector.
    for i in range(1, n + 1):
        multiply(v, i)
 
    # Find sum of digits in vector v[]
    sum = 0
    size = len(v)
    for i in range(size):
        sum += v[i]
    return sum
 
# Driver code
if __name__ == "__main__":
     
    n = 1000
    print(findSumOfDigits(n))
 
# This code is contributed by ita_c
C#



// C# program to find sum of digits in factorial
// of a number
using System;
using System.Collections;
class GFG{
// Function to multiply x with large number
// stored in vector v. Result is stored in v.
static ArrayList v=new ArrayList();
static void multiply(int x)
{
    int carry = 0;
    int size = v.Count;
    for (int i = 0 ; i < size ; i++)
    {
        // Calculate res + prev carry
        int res = carry + (int)v[i] * x;
 
        // updation at ith position
        v[i] = res % 10;
        carry = res / 10;
    }
    while (carry != 0)
    {
        v.Add(carry % 10);
        carry /= 10;
    }
}
 
// Returns sum of digits in n!
static int findSumOfDigits(int n)
{
    v.Add(1); // adds 1 to the end
 
    // One by one multiply i to current vector
    // and update the vector.
    for (int i=1; i<=n; i++)
        multiply(i);
 
    // Find sum of digits in vector v[]
    int sum = 0;
    int size = v.Count;
    for (int i = 0 ; i < size ; i++)
        sum += (int)v[i];
    return sum;
}
 
// Driver code
static void Main()
{
    int n = 1000;
    Console.WriteLine(findSumOfDigits(n));
}
}
// this code is contributed by mits
PHP



<?php
// PHP program to find sum of digits in
// factorial of a number
 
// Function to multiply x with large number
// stored in vector v. Result is stored in v.
function multiply(&$v, $x)
{
    $carry = 0;
    $size = count($v);
    for ($i = 0 ; $i < $size ; $i++)
    {
        // Calculate res + prev carry
        $res = $carry + $v[$i] * $x;
 
        // updation at ith position
        $v[$i] = $res % 10;
        $carry = (int)($res / 10);
    }
    while ($carry != 0)
    {
        array_push($v, $carry % 10);
        $carry = (int)($carry / 10);
    }
}
 
// Returns sum of digits in n!
function findSumOfDigits($n)
{
    $v = array(); // create a vector of type int
    array_push($v, 1); // adds 1 to the end
 
    // One by one multiply i to current vector
    // and update the vector.
    for ($i = 1; $i <= $n; $i++)
        multiply($v, $i);
 
    // Find sum of digits in vector v[]
    $sum = 0;
    $size = count($v);
    for ($i = 0 ; $i < $size ; $i++)
        $sum += $v[$i];
    return $sum;
}
 
// Driver code
$n = 1000;
print(findSumOfDigits($n));
 
// This code is contributed by mits
?>
Javascript



<script>
// Javascript program to find sum of digits in factorial
// of a number
     
    // Function to multiply x with large number
    // stored in vector v. Result is stored in v.
    let v=[];
    function multiply(x)
    {
        let carry = 0;
    let size = v.length;
    for (let i = 0 ; i < size ; i++)
    {
        // Calculate res + prev carry
        let res = carry + v[i] * x;
   
        // updation at ith position
        v[i]=res % 10;
        carry = Math.floor(res / 10);
    }
    while (carry != 0)
    {
        v.push(carry % 10);
        carry = Math.floor(carry/10);
    }
    }
     
    // Returns sum of digits in n!
    function findSumOfDigits(n)
    {
        v.push(1); // adds 1 to the end
   
    // One by one multiply i to current vector
    // and update the vector.
    for (let i=1; i<=n; i++)
        multiply(i);
   
    // Find sum of digits in vector v[]
    let sum = 0;
    let size = v.length;
    for (let i = 0 ; i < size ; i++)
        sum += v[i];
    return sum;
    }
     
    // Driver code
    let n = 1000;
    document.write(findSumOfDigits(n));
     
     
    // This code is contributed by avanitrachhadiya2155
</script>
Output: 
 
10539
 

My Personal Notes
arrow_drop_up
Previous
Find sum of factorials in an array
Next

Count digits in a factorial | Set 1
Recommended Articles
Page :
Find the last digit when factorial of A divides factorial of B
08, Oct 17
Find the last two digits of Factorial of a given Number
08, Jun 20
Smallest number with at least n digits in factorial
23, Jan 17
Number of digits in N factorial to the power N
03, Jun 18
Numbers of Length N having digits A and B and whose sum of digits contain only digits A and B
31, Jan 19
Find the Largest number with given number of digits and sum of digits
06, Jun 16
Find smallest number with given number of digits and sum of digits under given constraints
26, Jan 20
Count digits in a factorial | Set 2
12, Jul 16
Count digits in a factorial | Set 1
12, Jul 16
Find smallest number with given digits and sum of digits
10, Aug 21
Number formed by deleting digits such that sum of the digits becomes even and the number odd
26, Feb 20
Check if sum of digits of a number exceeds the product of digits of that number
13, May 21
Minimum digits to be removed to make either all digits or alternating digits same
15, Aug 20
Find sum of factorials till N factorial (1! + 2! + 3! + ... + N!)
16, Dec 21
Sum of divisors of factorial of a number
07, Jun 17
Check if a subarray of length K with sum equal to factorial of a number exists or not
22, Sep 20
Find the first natural number whose factorial is divisible by x
12, Jan 17
Find maximum power of a number that divides a factorial
14, Jan 18
Find the length of factorial of a number in any given base
30, Mar 20
Python program to find the factorial of a number using recursion
05, Nov 20
Find remainder when a number A raised to N factorial is divided by P
13, Aug 21
Recursive Program to find Factorial of a large number
13, Dec 21
Check if a given number is factorial of any number
20, Nov 19
Check if sum of digits in the left half is divisible by sum of digits in the right half in the largest permutation of N
15, Jun 21
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
GeeksforGeeks
Vote for difficulty
Current difficulty :
Medium





Improved By :
Article Tags :
Practice Tags :
Report Issue

We use cookies to ensure you have the best browsing experience on our website. By using our site, you
acknowledge that you have read and understood our
Cookie Policy &
        Privacy Policy

Lightbox

Start Your Coding Journey Now!