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 elementint 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 codeint main(){    int n = 7;     cout << findThirdDigit(n);      return 0;}

Java

 // Java implementation of the// above approachclass GFG{     // Function to find the elementstatic 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 codepublic 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 elementdef 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 coden = 7print(findThirdDigit(n)) # This code is contributed# by Shrikant13

C#

 // C# implementation of the above approachusing System; class GFG{     // Function to find the elementstatic 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 codestatic void Main(){    int n = 7;     Console.WriteLine(findThirdDigit(n));}} // This code is contributed by mits



Javascript


Output:
1

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