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# Check if a given number divides the sum of the factorials of its digits

• Last Updated : 20 May, 2021

Given an integer N, the task is to check whether N divides the sum of the factorials of its digits.

Examples:

Input: N = 19
Output: Yes
1! + 9! = 1 + 362880 = 362881, which is divisible by 19.

Input: N = 20
Output: No
0! + 2! = 1 + 4 = 5, which is not divisible by 20.

Approach: First, store the factorials of all the digits from 0 to 9 in an array. And, for the given number N check if it divides the sum of the factorials of its digits.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function that returns true if n divides``// the sum of the factorials of its digits``bool` `isPossible(``int` `n)``{` `    ``// To store factorials of digits``    ``int` `fac;``    ``fac = fac = 1;` `    ``for` `(``int` `i = 2; i < 10; i++)``        ``fac[i] = fac[i - 1] * i;` `    ``// To store sum of the factorials``    ``// of the digits``    ``int` `sum = 0;` `    ``// Store copy of the given number``    ``int` `x = n;` `    ``// Store sum of the factorials``    ``// of the digits``    ``while` `(x) {``        ``sum += fac[x % 10];``        ``x /= 10;``    ``}` `    ``// If it is divisible``    ``if` `(sum % n == 0)``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``int` `main()``{``    ``int` `n = 19;` `    ``if` `(isPossible(n))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{``    ` `    ``// Function that returns true if n divides``    ``// the sum of the factorials of its digits``    ``static` `boolean` `isPossible(``int` `n)``    ``{``    ` `        ``// To store factorials of digits``        ``int` `fac[] = ``new` `int``[``10``];``        ``fac[``0``] = fac[``1``] = ``1``;``    ` `        ``for` `(``int` `i = ``2``; i < ``10``; i++)``            ``fac[i] = fac[i - ``1``] * i;``    ` `        ``// To store sum of the factorials``        ``// of the digits``        ``int` `sum = ``0``;``    ` `        ``// Store copy of the given number``        ``int` `x = n;``    ` `        ``// Store sum of the factorials``        ``// of the digits``        ``while` `(x != ``0``)``        ``{``            ``sum += fac[x % ``10``];``            ``x /= ``10``;``        ``}``    ` `        ``// If it is divisible``        ``if` `(sum % n == ``0``)``            ``return` `true``;``    ` `        ``return` `false``;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``19``;``    ` `        ``if` `(isPossible(n))``            ``System.out.println(``"Yes"``);``        ``else``            ``System.out.println(``"No"``);``    ` `    ``}``}` `// This code is contributed by Ryuga`

## Python3

 `# Python 3 implementation of the approach` `# Function that returns true if n divides``# the sum of the factorials of its digits``def` `isPossible(n):``    ` `    ``# To store factorials of digits``    ``fac ``=` `[``0` `for` `i ``in` `range``(``10``)]``    ``fac[``0``] ``=` `1``    ``fac[``1``] ``=` `1` `    ``for` `i ``in` `range``(``2``, ``10``, ``1``):``        ``fac[i] ``=` `fac[i ``-` `1``] ``*` `i` `    ``# To store sum of the factorials``    ``# of the digits``    ``sum` `=` `0` `    ``# Store copy of the given number``    ``x ``=` `n` `    ``# Store sum of the factorials``    ``# of the digits``    ``while` `(x):``        ``sum` `+``=` `fac[x ``%` `10``]``        ``x ``=` `int``(x ``/` `10``)` `    ``# If it is divisible``    ``if` `(``sum` `%` `n ``=``=` `0``):``        ``return` `True` `    ``return` `False` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``n ``=` `19` `    ``if` `(isPossible(n)):``        ``print``(``"Yes"``)``    ``else``:``        ``print``(``"No"``)` `# This code is contributed by``# Surendra_Gangwar`

## C#

 `// C# implementation of the approach``using` `System;``class` `GFG``{``    ` `    ``// Function that returns true if n divides``    ``// the sum of the factorials of its digits``    ``static` `bool` `isPossible(``int` `n)``    ``{``    ` `        ``// To store factorials of digits``        ``int``[] fac = ``new` `int``;``        ``fac = fac = 1;``    ` `        ``for` `(``int` `i = 2; i < 10; i++)``            ``fac[i] = fac[i - 1] * i;``    ` `        ``// To store sum of the factorials``        ``// of the digits``        ``int` `sum = 0;``    ` `        ``// Store copy of the given number``        ``int` `x = n;``    ` `        ``// Store sum of the factorials``        ``// of the digits``        ``while` `(x != 0)``        ``{``            ``sum += fac[x % 10];``            ``x /= 10;``        ``}``    ` `        ``// If it is divisible``        ``if` `(sum % n == 0)``            ``return` `true``;``    ` `        ``return` `false``;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main ()``    ``{``        ``int` `n = 19;``    ` `        ``if` `(isPossible(n))``            ``Console.WriteLine(``"Yes"``);``        ``else``            ``Console.WriteLine(``"No"``);``    ``}``}` `// This code is contributed by Code_Mech.`

## PHP

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## Javascript

 ``
Output:
`Yes`

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