Square-free Number in C

Square-free number

A square-free number is a natural number that contains no powers greater than 1 in its prime factorization. In other words, if $x$ is our number, and is the prime factorization of $x$ into $r$ distinct primes, then $a_i\ge 2$ is always false for square-free $x$.

Note: we assume here that $x$ itself must be greater than 1; hence 1 is not considered square-free. However, one must be alert to the particular context in which “square-free” is used as to whether this is considered the case.

The name derives from the fact that if any $a_i$ were to be greater than or equal to two, we could be sure that at least one square divides $x$ (namely, $p_i^2$.)

A number is called a square free number if there does not exist a number greater than 1, whose square divides the number evenly/perfectly. For example, number 8 is not a square free number as number 4 (which is square of 2), divides 8. Similarly, number 4 is also not a square free number. However numbers 1, 3, 6 all are square free numbers.

Code of Square- free Number: C program !

#include

int isSquareFree(int n)

{

    int i;

    for(i=2;i<=n; i++)

        if(n%i==0)

            if(n%(i*i)==0)

                return 0;

    return 1;

}

int main()

{

    int number;

loop:

    printf("Enter a number to check it's a Square-free Number or not: ");

    scanf("%d",&number);

    if(isSquareFree(number)==1)

        printf("Square-free Number!\n\n");

    else

        printf("Not Square-free Number!\n\n");

    goto loop;

    return 0;

}

Output:

Enter a number to check it's a Square-free Number or not:6

Square-free Number!

Enter a number to check it's a Square-free Number or not:9

Not Square-free Number!

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