Find unit digit of x raised to power y

Given two numbers x and y, find unit digit of x^y.

Examples :

Input  : x = 2, y = 1
Output : 2
Explanation
2^1 = 2 so units digit is 2.

Input : x = 4, y = 2
Output : 6
Explanation
4^2 = 16 so units digit is 6.

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

Method 1 (Simple) Compute value of x^y and find its last digit. This method causes overflow for slightly larger values of x and y.

Method 2 (Efficient)
1) Find last digit of x.
2) Compute x^y under modulo 10 and return its value.

C++

// Efficient C++ program to 
// find unit digit of x^y. 
#include <bits/stdc++.h> 
using namespace std; 
  
// Returns unit digit of x 
// raised to power y 
int unitDigitXRaisedY(int x, int y) 
{ 
    // Initialize result as 1 to 
    // handle case when y is 0. 
    int res = 1; 
  
    // One by one multiply with x 
    // mod 10 to avoid overflow. 
    for (int i = 0; i < y; i++) 
        res = (res * x) % 10; 
  
    return res; 
} 
  
// Driver program 
int main() 
{   
   cout << unitDigitXRaisedY(4, 2); 
   return 0; 
} 

Java

// Efficient Java program to find  
// unit digit of x^y. 
import java.io.*; 
  
class GFG { 
    // Returns unit digit of x raised to power y 
    static int unitDigitXRaisedY(int x, int y) 
    { 
        // Initialize result as 1 to 
        // handle case when y is 0. 
        int res = 1; 
      
        // One by one multiply with x 
        // mod 10 to avoid overflow. 
        for (int i = 0; i < y; i++) 
            res = (res * x) % 10; 
      
        return res; 
    } 
      
    // Driver program 
    public static void main(String args[])throws IOException 
    {  
    System.out.println(unitDigitXRaisedY(4, 2)); 
    } 
} 
  
// This code is contributed by Nikita Tiwari. 

Python3

# Python3 code to find 
# unit digit of x^y. 
  
# Returns unit digit of 
# x raised to power y 
def unitDigitXRaisedY( x , y ): 
  
    # Initialize result as 1 to 
    # handle case when y is 0. 
    res = 1
      
    # One by one multiply with x 
    # mod 10 to avoid overflow. 
    for i in range(y): 
        res = (res * x) % 10
      
    return res 
      
# Driver program 
print( unitDigitXRaisedY(4, 2)) 
  
  
# This code is contributed by Abhishek Sharma44. 

C#

// Efficient Java program to find  
// unit digit of x^y. 
using System; 
  
class GFG  
{ 
    // Returns unit digit of x raised to power y 
    static int unitDigitXRaisedY(int x, int y) 
    { 
        // Initialize result as 1 to 
        // handle case when y is 0. 
        int res = 1; 
      
        // One by one multiply with x 
        // mod 10 to avoid overflow. 
        for (int i = 0; i < y; i++) 
            res = (res * x) % 10; 
      
        return res; 
    } 
      
    // Driver program 
    public static void Main() 
    {  
    Console.WriteLine(unitDigitXRaisedY(4, 2)); 
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// Efficient PHP program to 
// find unit digit of x^y. 
  
// Returns unit digit of x 
// raised to power y 
function unitDigitXRaisedY($x, $y) 
{ 
    // Initialize result as 1 to 
    // handle case when y is 0. 
    $res = 1; 
  
    // One by one multiply with x 
    // mod 10 to avoid overflow. 
    for ($i = 0; $i < $y; $i++) 
        $res = ($res * $x) % 10; 
  
    return $res; 
} 
  
// Driver Code 
echo(unitDigitXRaisedY(4, 2)); 
  
// This code is contributed by Ajit. 
?> 

Output :

Further Optimizations: We can compute modular power in Log y.

Method 3 (Direct based on cyclic nature of last digit)
This method depends on the cyclicity with the last digit of x that is

x   |  power 2  |  power 3  |   power 4  | Cyclicity  
0   | .................................. |  .... repeat with 0
1   | .................................. |  .... repeat with 1
2   |     4     |     8     |      6     | .... repeat with 2
3   |     9     |     7     |      1     | .... repeat with 3
4   |     6     |....................... |  .... repeat with 4
5   | .................................. |  .... repeat with 5
6   | .................................. |  .... repeat with 6
7   |     9     |     3     |      1     | .... repeat with 7
8   |     4     |     2     |      6     | .... repeat with 8
9   |     1     | ...................... |  .... repeat with 9

So here we directly mod the power y with 4 because this is the last power after this all number’s repetition start
after this we simply power with number x last digit then we get the unit digit of produced number.

C++

// CPP code to find the unit digit of x  
// raised to power y. 
#include<iostream> 
#include<math.h> 
using namespace std; 
  
// find unit digit 
int unitnumber(int x, int y) 
{ 
    // Get last digit of x 
    x = x % 10; 
        
    // Last cyclic modular value 
    if(y!=0) 
        y = y % 4 + 4; 
  
    // here we simply return the  
    // unit digit or the power  
    // of a number 
    return (((int)(pow(x, y))) % 10); 
} 
  
int main() 
{ 
    int x = 133, y = 5; 
      
    // get unit digit number here we pass  
    // the unit  digit of x and the last  
    // cyclicity number that is y%4 
    cout << unitnumber(x, y); 
   
    return 0; 
} 

Java

// Java code to find the unit  
// digit of x  raised to power y. 
import java.io.*; 
import java.util.*; 
  
class GFG { 
      
    // find unit digit 
    static int unitnumber(int x, int y) 
    { 
        // Get last digit of x 
        x = x % 10; 
              
        // Last cyclic modular value 
        if(y!=0) 
             y = y % 4 + 4; 
      
        // here we simply return the  
        // unit digit or the power  
        // of a number 
        return (((int)(Math.pow(x, y))) % 10); 
    } 
      
      
    public static void main (String[] args) 
    { 
        int x = 133, y = 5; 
      
        // get unit digit number here we pass  
        // the unit digit of x and the last  
        // cyclicity number that is y%4 
        System.out.println(unitnumber(x, y));  
      
    } 
} 
  
// This code is contributed by Gitanjali. 

Python3

# Python3 code to find the unit    
# digit of x raised to power y. 
import math 
  
# Find unit digit 
def unitnumber(x, y): 
  
    # Get last digit of x 
    x = x % 10
          
    # Last cyclic modular value 
    if y!=0: 
         y = y % 4 + 4
  
    # Here we simply return   
    # the unit digit or the   
    # power of a number 
    return (((int)(math.pow(x, y))) % 10) 
  
  
# Driver code  
x = 133; y = 5
      
# Get unit digit number here we pass  
# the unit digit of x and the last  
# cyclicity number that is y%4 
print(unitnumber(x, y)) 
  
  
# This code is contributed by Gitanjali. 

C#

// C# code to find the unit  
// digit of x raised to power y. 
using System; 
  
class GFG { 
      
    // find unit digit 
    static int unitnumber(int x, int y) 
    { 
        // Get last digit of x 
        x = x % 10; 
              
        // Last cyclic modular value 
        if(y!=0) 
             y = y % 4 + 4; 
      
        // here we simply return the  
        // unit digit or the power  
        // of a number 
        return (((int)(Math.Pow(x, y))) % 10); 
    } 
      
    // Driver code 
    public static void Main () 
    { 
        int x = 133, y = 5; 
      
        // get unit digit number here we pass  
        // the unit digit of x and the last  
        // cyclicity number that is y%4 
        Console.WriteLine(unitnumber(x, y));  
      
    } 
} 
  
// This code is contributed by vt_m. 

PHP

<?php 
// PHP code to find the unit  
// digit of x raised to power y. 
  
// find unit digit 
function unitnumber($x, $y) 
{ 
    // Get last digit of x 
    $x = $x % 10; 
      
    // Last cyclic modular value 
    if($y!=0) 
        $y = $y % 4 + 4; 
  
    // here we simply return the  
    // unit digit or the power  
    // of a number 
    return (((int)(pow($x, $y))) % 10); 
} 
  
// Driver code 
$x = 133; $y = 5; 
      
// get unit digit number here we pass  
// the unit digit of x and the last  
// cyclicity number that is y%4 
echo(unitnumber($x, $y)); 
  
// This code is contributed by Ajit. 
?> 

Output :

Thanks to DevanshuAgarwal for suggesting above solution.

How to handle large numbers?
Efficient method for Last Digit Of a^b for Large Numbers

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes

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

C++

Java

Python3

C#

PHP

C++

Java

Python3

C#

PHP

Recommended Posts: