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Minimum divisor of a number to make the number perfect cube
  • Last Updated : 22 Feb, 2021

Given a positive integer N, the task is to find the minimum divisor by which it shall be divided to make it a perfect cube. If N is already a perfect cube, then print 1.
Examples: 

Input : N = 128
Output : 2
By Dividing N by 2, we get 64 which is a perfect cube.

Input : n = 6
Output : 6
By Dividing N by 6, we get 1 which is a perfect cube.

Input : n = 64
Output : 1

Any number is a perfect cube if all prime factors of it appear in multiples of 3, as you can see in the below figure.  

Therefore, the idea is to find the prime factorization of N and find power of each prime factor. Now, find and multiply all the prime factors whose power is not divisible by 3 as primeFactor*power%3. The resultant of the multiplication is the answer.
Below is the implementation of the above approach:  

C++




// C++ program to find minimum number which divide n
// to make it a perfect cube
#include <bits/stdc++.h>
using namespace std;
 
// Returns the minimum divisor
int findMinNumber(int n)
{
    int count = 0, ans = 1;
 
    // Since 2 is only even prime, compute its
    // power seprately.
    while (n % 2 == 0) {
        count++;
        n /= 2;
    }
 
    // If count is not divisible by 3,
    // it must be removed by dividing
    // n by prime number power.
    if (count % 3 != 0)
        ans *= pow(2, (count % 3));
 
    for (int i = 3; i <= sqrt(n); i += 2) {
        count = 0;
        while (n % i == 0) {
            count++;
            n /= i;
        }
 
        // If count is not divisible by 3,
        // it must be removed by dividing
        // n by prime number power.
        if (count % 3 != 0)
            ans *= pow(i, (count % 3));
    }
 
    // if n is a prime number
    if (n > 2)
        ans *= n;
 
    return ans;
}
 
// Driven Program
int main()
{
    int n = 128;
    cout << findMinNumber(n) << endl;
    return 0;
}


Java




// Java program to find minimum number which divide n
// to make it a perfect cube
class GFG{
  
// Returns the minimum divisor
static int findMinNumber(int n)
{
    int count = 0, ans = 1;
  
    // Since 2 is only even prime, compute its
    // power seprately.
    while (n % 2 == 0) {
        count++;
        n /= 2;
    }
  
    // If count is not divisible by 3,
    // it must be removed by dividing
    // n by prime number power.
    if (count % 3 != 0)
        ans *= Math.pow(2, (count % 3));
  
    for (int i = 3; i <= Math.sqrt(n); i += 2) {
        count = 0;
        while (n % i == 0) {
            count++;
            n /= i;
        }
  
        // If count is not divisible by 3,
        // it must be removed by dividing
        // n by prime number power.
        if (count % 3 != 0)
            ans *= Math.pow(i, (count % 3));
    }
  
    // if n is a prime number
    if (n > 2)
        ans *= n;
  
    return ans;
}
  
// Driver code
public static void main(String[] args)
{
    int n = 128;
    System.out.print(findMinNumber(n) +"\n");
}
}
 
// This code is contributed by Rajput-Ji


Python3




# Python3 program to find minimum number which divide n
# to make it a perfect cube
 
# Returns the minimum divisor
def findMinNumber(n):
    count = 0;
    ans = 1;
 
    # Since 2 is only even prime, compute its
    # power seprately.
    while (n % 2 == 0):
        count+=1;
        n /= 2;
     
    # If count is not divisible by 3,
    # it must be removed by dividing
    # n by prime number power.
    if (count % 3 != 0):
        ans *= pow(2, (count % 3));
 
    for i in range(3, int(pow(n, 1/2)), 2):
        count = 0;
        while (n % i == 0):
            count += 1;
            n /= i;
         
        # If count is not divisible by 3,
        # it must be removed by dividing
        # n by prime number power.
        if (count % 3 != 0):
            ans *= pow(i, (count % 3));
     
    # if n is a prime number
    if (n > 2):
        ans *= n;
 
    return ans;
 
# Driver code
if __name__ == '__main__':
    n = 128;
    print(findMinNumber(n));
 
# This code is contributed by 29AjayKumar


C#




// C# program to find minimum number which divide n
// to make it a perfect cube
using System;
 
class GFG{
   
// Returns the minimum divisor
static int findMinNumber(int n)
{
    int count = 0, ans = 1;
   
    // Since 2 is only even prime, compute its
    // power seprately.
    while (n % 2 == 0) {
        count++;
        n /= 2;
    }
   
    // If count is not divisible by 3,
    // it must be removed by dividing
    // n by prime number power.
    if (count % 3 != 0)
        ans *= (int)Math.Pow(2, (count % 3));
   
    for (int i = 3; i <= Math.Sqrt(n); i += 2) {
        count = 0;
        while (n % i == 0) {
            count++;
            n /= i;
        }
   
        // If count is not divisible by 3,
        // it must be removed by dividing
        // n by prime number power.
        if (count % 3 != 0)
            ans *= (int)Math.Pow(i, (count % 3));
    }
   
    // if n is a prime number
    if (n > 2)
        ans *= n;
   
    return ans;
}
   
// Driver code
public static void Main(String[] args)
{
    int n = 128;
    Console.Write(findMinNumber(n) +"\n");
}
}
 
// This code is contributed by 29AjayKumar


Output: 

2

 

Time Complexity: O(sqrt(n))

Auxiliary Space: O(1)

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