# Third last digit in 5^N for given N

Given a positive integer N. The task is to find the value of the 3^{rd} digit from the last (right-most) of 5^{N}.

**Examples:**

Input :N = 6Output :6 Explanation : Value of 5^{6}= 15625.Input :N = 3Output :1 Explanation : Value of 5^{3}= 125.

**Approach:** Before moving to the actual approach, some facts regarding number theory are listed below as:

- 5
^{3}is the smallest 3-digit number which is a power of 5. - As 125 * 5 = 625, this concludes that multiple of number (ending with 125) with 5 always construct 625 as of last three digits of the result.
- Again as, 625 * 5 = 3125, this concludes that multiple numbers (ending with 625) with 5 always construct 125 as the last three digits of the result.

Hence, the final general solution is :

Case 1: if

n < 3, answer = 0.

Case 2: ifn >= 3 and is even,answer = 6.

Case 3: ifn >= 3 and is odd,answer = 1.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the element` `int` `findThirdDigit(` `int` `n)` `{` ` ` `// if n < 3` ` ` `if` `(n < 3)` ` ` `return` `0;` ` ` `// If n is even return 6` ` ` `// If n is odd return 1` ` ` `return` `n & 1 ? 1 : 6;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 7;` ` ` `cout << findThirdDigit(n);` ` ` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the` `// above approach` `class` `GFG` `{` ` ` `// Function to find the element` `static` `int` `findThirdDigit(` `int` `n)` `{` ` ` `// if n < 3` ` ` `if` `(n < ` `3` `)` ` ` `return` `0` `;` ` ` `// If n is even return 6` ` ` `// If n is odd return 1` ` ` `return` `(n & ` `1` `) > ` `0` `? ` `1` `: ` `6` `;` `}` `// Driver code` `public` `static` `void` `main(String args[])` `{` ` ` `int` `n = ` `7` `;` ` ` `System.out.println(findThirdDigit(n));` `}` `}` `// This code is contributed` `// by Akanksha Rai` |

## Python3

`# Python3 implementation of the` `# above approach` `# Function to find the element` `def` `findThirdDigit(n):` ` ` `# if n < 3` ` ` `if` `n < ` `3` `:` ` ` `return` `0` ` ` `# If n is even return 6` ` ` `# If n is odd return 1` ` ` `return` `1` `if` `n ` `and` `1` `else` `6` `# Driver code` `n ` `=` `7` `print` `(findThirdDigit(n))` `# This code is contributed` `# by Shrikant13` |

## C#

`// C# implementation of the above approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the element` `static` `int` `findThirdDigit(` `int` `n)` `{` ` ` `// if n < 3` ` ` `if` `(n < 3)` ` ` `return` `0;` ` ` `// If n is even return 6` ` ` `// If n is odd return 1` ` ` `return` `(n & 1)>0 ? 1 : 6;` `}` `// Driver code` `static` `void` `Main()` `{` ` ` `int` `n = 7;` ` ` `Console.WriteLine(findThirdDigit(n));` `}` `}` `// This code is contributed by mits` |

## PHP

`<?php` `// PHP implementation of the above approach` `// Function to find the element` `function` `findThirdDigit(` `$n` `)` `{` ` ` `// if n < 3` ` ` `if` `(` `$n` `< 3)` ` ` `return` `0;` ` ` `// If n is even return 6` ` ` `// If n is odd return 1` ` ` `return` `$n` `& 1 ? 1 : 6;` `}` `// Driver code` `$n` `= 7;` `echo` `findThirdDigit(` `$n` `);` `// This code contributed by` `// PrinciRaj1992` `?>` |

## Javascript

`<script>` ` ` `// Javascript implementation of the above approach` `// Function to find the element` `function` `findThirdDigit(n)` `{` ` ` `// if n < 3` ` ` `if` `(n < 3)` ` ` `return` `0;` ` ` `// If n is even return 6` ` ` `// If n is odd return 1` ` ` `return` `n & 1 ? 1 : 6;` `}` `// Driver code` `var` `n = 7;` `document.write( findThirdDigit(n));` `</script>` |

**Output:**

1