# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• When we try to convert X into the base Y
• We repeatedly divide X by base Y and store the remainder.
• So the 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 lsat 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 ` `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 `

Output:

```1
```

Time Complexity: O(1)

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Improved By : AnkitRai01, Rajput-Ji