# Integer part of the geometric mean of the divisors of N

• Last Updated : 07 Mar, 2022

Given an integer N, the task is to find the integer part of the geometric mean of the divisors of N. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers), and so on.

Examples:
Input: N = 4
Output:
Divisors of 4 are 1, 2 and 4
Geometric mean = (1 * 2 * 4)(1/3) = 8(1/3) = 2
Input: N = 16
Output:
Divisors of 16 are 1, 2, 4, 8 and 16
Geometric mean = (1 * 2 * 4 * 8 * 16)(1/5) = 1024(1/5) = 4

Approach: It cane be observed that a series will be formed for the values of N as 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, ….. whose Nth term is ⌊√n⌋.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to return the integer` `// part of the geometric mean` `// of the divisors of n` `int` `geometricMean(``int` `n)` `{` `    ``return` `sqrt``(n);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 16;`   `    ``cout << geometricMean(n);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `class` `GFG ` `{`   `// Function to return the integer` `// part of the geometric mean` `// of the divisors of n` `static` `int` `geometricMean(``int` `n)` `{` `    ``return` `(``int``) Math.sqrt(n);` `}`   `// Driver code` `public` `static` `void` `main(String []args)` `{` `    ``int` `n = ``16``;` `    ``System.out.println(geometricMean(n));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach ` `from` `math ``import` `sqrt`   `# Function to return the integer ` `# part of the geometric mean ` `# of the divisors of n ` `def` `geometricMean(n) :`   `    ``return` `int``(sqrt(n)); `   `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `:`   `    ``n ``=` `16``; `   `    ``print``(geometricMean(n)); `   `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach` `using` `System;    `   `class` `GFG ` `{` ` `  `// Function to return the integer` `// part of the geometric mean` `// of the divisors of n` `static` `int` `geometricMean(``int` `n)` `{` `    ``return` `(``int``) Math.Sqrt(n);` `}` ` `  `// Driver code` `public` `static` `void` `Main(String []args)` `{` `    ``int` `n = 16;` `    ``Console.WriteLine(geometricMean(n));` `}` `}`   `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`4`

Time Complexity: O(1)

Auxiliary Space: O(1)

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