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