# Find last digit in factorial

Given a number n, we need to find the last digit in factorial n.

Input : n = 4
Output : 4
4! = 4 * 3 * 2 * 1. =  24.  Last digit of 24 is 4.

Input : n = 5
Output : 5
5! = 5*4 * 3 * 2 * 1. =  120.  Last digit of 120 is 0.

A Naive Solution is to first compute fact = n!, then return the last digit of the result by doing fact % 10.  This solution is inefficient and causes integer overflow for even slightly large value of n.

An Efficient Solution is based on the observation that all factorials after 5 have 0 as last digit.

1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
…………..

## C++

 `// C++ program to find last digit in ` `// factorial n. ` `#include ` `using` `namespace` `std; ` ` `  `int` `lastDigitFactorial(unsigned ``int` `n) ` `{ ` `   ``// Explicitly handle all numbers ` `   ``// less than or equal to 4 ` `   ``if` `(n == 0) ``return` `1; ` `   ``else` `if` `(n <= 2) ``return` `n; ` `   ``else` `if` `(n == 3) ``return` `6; ` `   ``else` `if` `(n == 4) ``return` `4; ` `   `  `   ``// For all numbers greater than 4 ` `   ``// the last digit is 0 ` `   ``else` `return` `0; ` `} ` ` `  `int` `main() { ` ` `  `    ``cout<

## Java

 `// Java program to find last   ` `// digit in factorial n. ` `import` `java.io.*;  ` `import` `java.util.*;  ` ` `  `class` `GFG {  ` `     `  `static` `int` `lastDigitFactorial(``int` `n) ` `{ ` `     `  `    ``// Explicitly handle all numbers ` `    ``// less than or equal to 4 ` `    ``if` `(n == ``0``) ``return` `1``; ` `    ``else` `if` `(n <= ``2``) ``return` `n; ` `    ``else` `if` `(n == ``3``) ``return` `6``; ` `    ``else` `if` `(n == ``4``) ``return` `4``; ` `     `  `    ``// For all numbers greater than ` `    ``// 4 the last digit is 0 ` `    ``else` `return` `0``; ` `} ` ` `  `// Driver code  ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``System.out.println(lastDigitFactorial(``6``)); ` `}  ` `}  ` ` `  `// This code is contributed by coder001 `

## Python3

 `# Python3 program to find last digit in  ` `# factorial n. ` ` `  `def` `lastDigitFactorial(n): ` `     `  `    ``# Explicitly handle all numbers  ` `    ``# less than or equal to 4  ` `    ``if` `(n ``=``=` `0``): ``return` `1` `    ``elif` `(n <``=` `2``): ``return` `n  ` `    ``elif` `(n ``=``=` `3``): ``return` `6` `    ``elif` `(n ``=``=` `4``): ``return` `4` `     `  `    ``# For all numbers greater than 4  ` `    ``# the last digit is 0  ` `    ``else``: ``return` `0` ` `  `print``(lastDigitFactorial(``6``)) ` ` `  `# This code is contributed by divyeshrabadiya07 `

## C#

 `// C# program to find last  ` `// digit in factorial n.  ` `using` `System; ` `class` `GFG{  ` `     `  `static` `int` `lastDigitFactorial(``int` `n)  ` `{  ` `     `  `    ``// Explicitly handle all numbers  ` `    ``// less than or equal to 4  ` `    ``if` `(n == 0) ``return` `1;  ` `    ``else` `if` `(n <= 2) ``return` `n;  ` `    ``else` `if` `(n == 3) ``return` `6;  ` `    ``else` `if` `(n == 4) ``return` `4;  ` `     `  `    ``// For all numbers greater than  ` `    ``// 4 the last digit is 0  ` `    ``else` `return` `0;  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main(``string``[] args)  ` `{  ` `    ``Console.Write(lastDigitFactorial(6));  ` `}  ` `}  ` ` `  `// This code is contributed by rutvik_56 `

Output:

```0
```

Time Complexity : O(1)
Auxiliary Space : O(1)

Now try below problems

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