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.*/ ` |

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**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 ` ` ` |

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**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!