Please login

Prime

Prepinsta Prime

Video courses for company/skill based Preparation

(Check all courses)
Get Prime Video
Prime

Prepinsta Prime

Purchase mock tests for company/skill building

(Check all mocks)
Get Prime mock

C++ Program for Square Free Number

C++ Program for Square Free Number

Square Free Number Problem

TCS flagship contest, TCS CodeVita, has been expanding it’s horizon and raising the bar higher with each passing year. TCS believes that programming can be both fun and productive at the same time. Square Free Number problem is one of the  previous year question, here we have provided a solution in C++ language for the same.

Problem Description

In the theory of numbers, square free numbers have a special place.  A square free number is one that is not divisible by a perfect square (other than 1).  Thus 72 is divisible by 36 (a perfect square), and is not a square free number, but 70 has factors 1, 2, 5, 7, 10, 14, 35 and 70.  As none of these are perfect squares (other than 1), 70 is a square free number.

For some algorithms, it is important to find out the square free numbers that divide a number.  Note that 1 is not considered a square free number. 

In this problem, you are asked to write a program to find the number of square free numbers that divide a given number.

Input:-

  • The only line of the input is a single integer N which is divisible by no prime number larger than 19.

Output:-

  • One line containing an integer that gives the number of square free numbers (not including 1).

Constraints:-

  • N   < 10^9

Complexity:-

  • Simple

Time Limit:-

  • 1

Examples


Example 1

  • Input:-
    20
  • Output:-
    3

Explanation

N=20

If we list the numbers that divide 20, they are

1, 2, 4, 5, 10, 20

1 is not a square free number, 4 is a perfect square, and 20 is divisible by 4, a perfect square.  2 and 5, being prime, are square free, and 10 is divisible by 1,2,5 and 10, none of which are perfect squares.  Hence the square free numbers that divide 20 are 2, 5, 10.  Hence the result is 3.

Example 2

  • Input:-
    72
  • Output:-
    3

Explanation

N=72.  The numbers that divide 72 are

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

1 is not considered square free.   4, 9 and 36 are perfect squares, and 8,12,18,24 and 72 are divisible by one of the.  Hence only 2, 3 and 6 are square free.  (It is easily seen that none of them are divisible by a perfect square).  The result is 3.

C++ Code

#include  <iostream>
#include  <math.h>
using namespace std;

int main()
{
    long int n;
    double sqnum;
    long int i,j=0,flag,chksqr,temp[10000];
  	int count=0,k;
  	cout<<"Enter the number:";
    cin>>n;
    
    for(i=2;i<=n/2;i++)
    {
        if(n%i==0)
        {    
            count++;
            sqnum=sqrt(i);
            chksqr=sqnum;
            if(chksqr==sqnum)
            {
                count--;
                temp[j]=i;
                j++;
            }
            else
            {
                for(k=0;k<j;k++) { if(i>temp[k] && j!=0)
                    {
                        if(i%temp[k]==0)
                        {	
                          	count--;
                        	k=j+1;
                        }
                    }
                    else
                        break;
                }
            }
        }
    }

    cout<<count;
    return 0;
}
Output
Enter the number : 20
3

Square Free Number Problem in other Languages

JAVA

Sorry, we don’t the solution in Java You can provide the solution for this problem in Java, below in the comments sections.

C

To find the solution of To find the solution of Square Free Number problem in C Programming language click on the button below:

C

Python

Sorry, we don’t the solution in Python You can provide the solution for this problem in Python, below in the comments sections.