# Find the unit place digit of sum of N factorials

Given a number N, the task is to find units place digit of the first N natural numbers factorials, i.e. 1!+2!+3!+….N! where N<=10e18.

Examples:

```Input: n = 2
Output: 3
1! + 2! = 3
Last digit is 3

Input: n = 3
Output: 9
1! + 2! + 3! = 9
Last digit is 9
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach: In this approach, simply calculate factorial of each number and find sum of these. Finally get the unit place digit of sum. This will take a lot of time and unnecessary calculations.

Efficient Approach: In this approach, only unit’s digit of N is to be calculated in the range [1, 5], because:
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
so on.

As 5!=120, and factorial of number greater than 5 have trailing zeros. So, N>=5 doesn’t contribrute in unit place while doing sum.

Therefore:

```if (n < 5)
ans = (1 ! + 2 ! +..+ n !) % 10;
else
ans = (1 ! + 2 ! + 3 ! + 4 !) % 10;

Note : We know (1! + 2! + 3! + 4!) % 10 = 3
So we always return 3 when n is greater
than 4.
```

Below is the implementation of the efficient approach:

## C++

 `// C++ program to find the unit place digit ` `// of the first N natural numbers factorials ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the unit's place digit ` `int` `get_unit_digit(``long` `long` `int` `N) ` `{ ` ` `  `    ``// Let us write for cases when ` `    ``// N is smaller than or equal ` `    ``// to 4. ` `    ``if` `(N == 0 || N == 1) ` `       ``return` `1; ` `    ``else` `if` `(N == 2) ` `       ``return` `3; ` `    ``else`  `if` `(N == 3) ` `       ``return` `9; ` ` `  `    ``// We know following ` `    ``// (1! + 2! + 3! + 4!) % 10 = 3 ` `    ``else` `// (N >= 4)  ` `       ``return` `3; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``long` `long` `int` `N = 1; ` ` `  `    ``for` `(N = 0; N <= 10; N++) ` `        ``cout << ``"For N = "` `<< N ` `             ``<< ``" : "` `<< get_unit_digit(N) ` `             ``<< endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java  program to find the unit place digit  ` `// of the first N natural numbers factorials ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `     `  `// Function to find the unit's place digit  ` `static` `int` `get_unit_digit(  ``int` `N)  ` `{  ` ` `  `    ``// Let us write for cases when  ` `    ``// N is smaller than or equal  ` `    ``// to 4.  ` `    ``if` `(N == ``0` `|| N == ``1``)  ` `    ``return` `1``;  ` `    ``else` `if` `(N == ``2``)  ` `    ``return` `3``;  ` `    ``else` `if` `(N == ``3``)  ` `    ``return` `9``;  ` ` `  `    ``// We know following  ` `    ``// (1! + 2! + 3! + 4!) % 10 = 3  ` `    ``else` `// (N >= 4)  ` `    ``return` `3``;  ` `}  ` ` `  `// Driver code  ` `     `  `    ``public` `static` `void` `main (String[] args) { ` `         `  `      ``int` `N = ``1``;  ` ` `  `    ``for` `(N = ``0``; N <= ``10``; N++)  ` `            ``System.out.println (``"For N = "` `+ N  ` `            ``+ ``" : "` `+ get_unit_digit(N));  ` `    ``} ` `} ` `//This Code is Contributed by ajit `

## Python3

 `# Python3 program to find the unit ` `# place digit of the first N natural ` `# numbers factorials  ` ` `  `# Function to find the unit's place digit ` `def` `get_unit_digit(N): ` `     `  `    ``# Let us write for cases when  ` `    ``# N is smaller than or equal  ` `    ``# to 4.  ` `    ``if` `(N ``=``=` `0` `or` `N ``=``=` `1``): ` `        ``return` `1` `    ``elif` `(N ``=``=` `2``): ` `        ``return` `3` `    ``elif``(N ``=``=` `3``): ` `        ``return` `9` `         `  `    ``# We know following  ` `    ``# (1! + 2! + 3! + 4!) % 10 = 3 ` `    ``else``: ` `        ``return` `3` ` `  `# Driver code ` `N ``=` `1` `for` `N ``in` `range``(``11``): ` `    ``print``(``"For N = "``, N, ``":"``, ` `        ``get_unit_digit(N), sep ``=` `' '``) ` ` `  `# This code is contributed  ` `# by sahilshelangia `

## C#

 `// C# program to find the unit  ` `// place digit of the first N  ` `// natural numbers factorials ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to find the unit's ` `// place digit  ` `static` `int` `get_unit_digit( ``int` `N)  ` `{  ` ` `  `    ``// Let us write for cases when  ` `    ``// N is smaller than or equal  ` `    ``// to 4.  ` `    ``if` `(N == 0 || N == 1)  ` `    ``return` `1;  ` `    ``else` `if` `(N == 2)  ` `    ``return` `3;  ` `    ``else` `if` `(N == 3)  ` `    ``return` `9;  ` ` `  `    ``// We know following  ` `    ``// (1! + 2! + 3! + 4!) % 10 = 3  ` `    ``else` `// (N >= 4)  ` `    ``return` `3;  ` `}  ` ` `  `// Driver code  ` `static` `public` `void` `Main () ` `{ ` `    ``int` `N = 1;  ` ` `  `    ``for` `(N = 0; N <= 10; N++)  ` `        ``Console.WriteLine (``"For N = "` `+ N + ` `                ``" : "` `+ get_unit_digit(N));  ` `} ` `} ` ` `  `// This Code is Contributed by akt_mit `

## PHP

 `= 4)  ` `        ``return` `3; ` `} ` ` `  `// Driver code ` `\$N` `= 1; ` ` `  `for` `(``\$N` `= 0; ``\$N` `<= 10; ``\$N``++) ` `    ``echo` `"For N = "` `. ``\$N``. ` `         ``" : "` `. get_unit_digit(``\$N``) . ``"\n"``; ` ` `  `// This code is contributed  ` `// by ChitraNayal ` `?> `

Output:

```For N = 0 : 1
For N = 1 : 1
For N = 2 : 3
For N = 3 : 9
For N = 4 : 3
For N = 5 : 3
For N = 6 : 3
For N = 7 : 3
For N = 8 : 3
For N = 9 : 3
For N = 10 : 3
```

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