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# Third last digit in 5^N for given N

• Last Updated : 29 Apr, 2021

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

Examples:

```Input : N = 6
Output : 6
Explanation : Value of 56 = 15625.

Input : N = 3
Output : 1
Explanation : Value of 53 = 125. ```

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

• 53 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: if n >= 3 and is even, answer = 6.
Case 3: if n >= 3 and is odd, answer = 1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ``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

 ``

## Javascript

 ``
Output:
`1`

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