C function to determine if a number is a prime number

  • Write a C function that returns true if the input is a prime number and returns false otherwise: 

    int isPrime(int n)
{
    int isPr = 1;   // 1 = True

    for ( int i = 2; i < n; i++ )
    {
        if ( n%i == 0 )
        {
            isPr = 0;  // n is not prime
            break;
        }
    }

    return isPr;
}

     

C function to determine if a number is a prime number

  • Write a C function that returns true if the input is a prime number and returns false otherwise: 

    int isPrime(int n)
{
    int isPr = 1;   // 1 = True

    for ( int i = 2; i < n; i++ )
    {
        if ( n%i == 0 )
        {
            isPr = 0;  // n is not prime
            break;
        }
    }

    return isPr;
}

    The return type of the function is int (that's how C usually represent boolean values)

C function to determine if a number is a prime number

  • Write a C function that returns true if the input is a prime number and returns false otherwise: 

    int isPrime(int n)
{
    int isPr = 1;   // 1 = True

    for ( int i = 2; i < n; i++ )
    {
        if ( n%i == 0 )
        {
            isPr = 0;  // n is not prime
            break;
        }
    }

    return isPr;
}

    We initially assumes that the input n is a prime number (and check this assumption next).

C function to determine if a number is a prime number

  • Write a C function that returns true if the input is a prime number and returns false otherwise: 

    int isPrime(int n)
{
    int isPr = 1;   // 1 = True

    for ( int i = 2; i < n; i++ )
    {
        if ( n%i == 0 )
        {
            isPr = 0;  // n is not prime
            break;
        }
    }

    return isPr;
}

    We check if n is prime by divide it by every possible divisor...
     

C function to determine if a number is a prime number

  • Write a C function that returns true if the input is a prime number and returns false otherwise: 

    int isPrime(int n)
{
    int isPr = 1;   // 1 = True

    for ( int i = 2; i < n; i++ )
    {
        if ( n%i == 0 )
        {
            isPr = 0;  // n is not prime
            break;
        }
    }

    return isPr;
}

    If we find a divisor for n, then it is not prime and we can stop
     

C function to determine if a number is a prime number

  • Write a C function that returns true if the input is a prime number and returns false otherwise: 

    int isPrime(int n)
{
    int isPr = 1;   // 1 = True

    for ( int i = 2; i < n; i++ )
    {
        if ( n%i == 0 )
        {
            isPr = 0;  // n is not prime
            break;
        }
    }

    return isPr;
}

    When the loop finishes, we return the result
     

DEMO: demo/C/set1/c-prog1.c

Factoring an integer number

  • Every integer number can be factored into its prime number factors

  • The prime number factors of a number x are prime numbers whose product is equal to the number x

  • Example: 

     The prime factors of  6 are: 2  3       (2 × 3 = 6)
   
 The prime factors of 12 are: 2  2  3    (2 × 2 × 3 = 12)

 The prime factors of 90 are: 2  3  3  5 (2 × 3 × 3 × 5 = 180)

  • Write a C program that reads in an integer number and prints out its prime factors

Factoring an integer number

  • Develop a plan: 

       How do you factor the number 60 ?:

     60 = ???

Factoring an integer number

  • Develop a plan: 

       How do you factor the number 60 ?:

     60 = ???

 (1) Try dividing by 2: 60%2 == 0  --> 2 is a factor
     60/2 = 30  ===> now factor 30 
     
 (2) Try dividing by 2: 30%2 == 0  --> 2 is a factor
     30/2 = 15  ===> now factor 15

 (3) Try dividing by 2: 15%2 == 1  --> no more 2's, try next factor

 (4) Try dividing by 3: 15%3 == 0  --> 3 is a factor
     15/3 = 5   ===> now factor 5 

 (5) Try dividing by 3:  5%3 == 2  --> no more 3's, try next factor

 (6) Try dividing by 4:  5%4 == 1  --> no more 4's, try next factor

 (7) Try dividing by 5:  5%5 == 0  --> 5 is a factor
     5/5 = 1  ===> 1 cannot be factored -- STOP

Factoring an integer number

  • Write out the steps of the plan: 

       Read in number from input;

 nextFactor = 2;

 while ( number != 1 )
 {
    if ( number is divisible by nextFactor )
    {
        print nextFactor;
        reduce number to   number/nextFactor
    }
    else
    {
        try nextFactor+1 as nextFactor
    }
 }

Factoring an integer number

  • Translate the steps of the plan to C code: 

      #include <stdio.h>

int main(int argc, char *argv[])
{

    int x;
    int nextFactor;
       
    printf("Enter a number: ");
    scanf("%d", &x);

    nextFactor = 2; // Initialize nextFactor

    while ( x != 1 )
    {
        if ( x%nextFactor == 0 )
        {
            printf("%d\n", nextFactor); // Pront new factor
            x = x / nextFactor;         // Remove factor from number
        }
        else
            nextFactor = nextFactor+1;  // Try next factor
    }
}

DEMO: demo/C/set1/c-prog2.c