# 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 = 7Output:3 10 is 13 in base 9 with last digit 3Input:X = 55, Y = 3Output: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 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 <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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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**Output:**

1

**Time Complexity:** O(1)

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