Python Program for Check if count of divisors is even or odd

Last Updated : 30 Nov, 2018

Given a number “n”, find its total number of divisors are even or odd.

Examples :

Input  : n = 10      
Output : Even

Input:  n = 100
Output: Odd

Input:  n = 125
Output: Even

A naive approach would be to find all the divisors and then see if the total number of divisors is even or odd.

Time complexity for such a solution would be O(sqrt(n))

# Naive Solution to  
# find if count of  
# divisors is even 
# or odd 
import math 
  
# Function to count  
# the divisors 
def countDivisors(n) : 
      
    # Initialize count  
    # of divisors 
    count = 0
  
    # Note that this loop  
    # runs till square  
    # root 
    for i in range(1, (int)(math.sqrt(n)) + 2) : 
        if (n % i == 0) : 
              
            # If divisors are 
            # equal,increment 
            # count by one 
            # Otherwise increment 
            # count by 2 
            if( n // i == i) : 
                count = count + 1
            else : 
                count = count + 2
  
    if (count % 2 == 0) : 
        print("Even") 
    else : 
        print("Odd") 
  
  
# Driver program to test above function */ 
print("The count of divisor: ") 
countDivisors(10) 
  
#This code is contributed by Nikita Tiwari.*/ 

Output :

The count of divisor: Even

Efficient Solution:
We can observe that the number of divisors is odd only in case of perfect squares. Hence the best solution would be to check if the given number is perfect square or not. If it\’s a perfect square, then the number of divisors would be odd, else it\’d be even.

# Python program for 
# Efficient Solution to find 
# find if count of divisors 
# is even or odd 
  
# Python program for 
# Efficient Solution to find 
# find if count of divisors 
# is even or odd 
  
def NumOfDivisor(n): 
    if n < 1: 
        return
    root_n = n**0.5
      
    # If n is a perfect square, 
    # then it has odd divisors 
    if root_n**2 == n: 
        print("Odd") 
    else: 
        print("Even") 
          
# Driver code      
if __name__ == '__main__': 
    print("The count of divisor"+
        "of 10 is: ") 
    NumOfDivisor(10) 
      
# This code is contributed by Yt R  
   

Output :

The count of divisorof 10 is: 
Even

Please refer complete article on Check if count of divisors is even or odd for more details!

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