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Program to find the last digit of X in base Y
  • Last Updated : 06 Apr, 2021

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
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)

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