Program to find the last digit of X in base Y

Given a positive integer X and Y, the task is to find the last digit of X in the given base Y.

Examples:

Input: X = 10, Y = 7
Output: 3
10 is 13 in base 9 with last digit 3

Input: X = 55, Y = 3
Output: 1
55 is 3 in base 601 with last digit 1

Approach:

• When we try to convert X into the base Y
• We repeatedly divide X by base Y and store the remainder.
• So final result comprises of the remainders in the order of division steps.
• Lets say the remainder of division step 1 is p, step 2 is q, step 3 is r
• Then the resultant number in base Y will be rqp
• And the last digit will be p
• Therefore, we just need to find the first remainder of X when divided by Y to get the last digit in X in base Y. 
  

last digit = X % Y

Below is the implementation of the above approach:

C++

// C++ Program to find
// the last digit of X in base Y

#include <bits/stdc++.h>
using namespace std;

// Function to find the last
// digit of X in base Y
void last_digit(int X, int Y)
{
    cout << X % Y;
}

// Driver code
int main()
{
    int X = 55, Y = 3;
    last_digit(X, Y);
    return 0;
}

Java

// Java Program to find
// the last digit of X in base Y
import java.io.*;
public class GFG
{

// Function to find the last
// digit of X in base Y
static void last_digit(int X, int Y)
{
    System.out.print(X % Y);
}

// Driver code
public static void main(String []args)
{
    int X = 55, Y = 3;
    last_digit(X, Y);
}
}

// This code is contributed by Rajput-Ji

Python3

# Python3 Program to find
# the last digit of X in base Y

# Function to find the last
# digit of X in base Y
def last_digit(X, Y) :

    print(X % Y);

# Driver code
if __name__ == "__main__" :

    X = 55; Y = 3;
    last_digit(X, Y);

# This code is contributed
# by AnkitRai01

C#

// C# Program to find the last digit
// of X in base Y
using System;

class GFG
{

// Function to find the last
// digit of X in base Y
static void last_digit(int X, int Y)
{
    Console.Write(X % Y);
}

// Driver code
public static void Main(String []args)
{
    int X = 55, Y = 3;
    last_digit(X, Y);
}
}

// This code is contributed by Rajput-Ji

PHP

<?php
// PHP Program to find the last digit
// of X in base Y


// Function to find the last
// digit of X in base Y
function last_digit($X,$Y){

  echo( $X % $Y );

}

// Driver code

$X = 55;
$Y = 3;

last_digit($X,$Y);


?>

Javascript

<script>

// Javascript Program to find
// the last digit of X in base Y

// Function to find the last
// digit of X in base Y
function last_digit(X, Y)
{
    document.write(X % Y);
}

// Driver code
var X = 55, Y = 3;
last_digit(X, Y);

</script>

Output:

1

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