''' Purpose: continue introduction to functions
'''

def is_factor( x, y ) :
    ''' Determines whether y is a factor x
    '''
    # print( a1, b1 ) This won't work because a1 and b1 are variables over in the main code, so they don't exist
    # in this function
    rem = x % y
    if ( rem == 0 ) :
        result = True
    else: 
        result = False

    return result

def are_relative_primes( x, y ) :
    ''' Determines whether x and y are relatively prime; i.e., whether y
        is not a factor of x and vice-versa
    '''

    y_is_factor_of_x = is_factor( x, y )
    x_is_factor_of_y = is_factor( y, x )

    if ( y_is_factor_of_x == True ):
        result = False
    elif ( x_is_factor_of_y == True ):
        result = False
    else:
        result = True

    return result


def is_prime( x ) :
    ''' Determines whether x is a prime number; i.e., its only factors are
        1 and itself
    '''

    # have I found any reason to suspect x is not prime? No
    result = True

    # I need to check all numbers between 2 and n-1 to see if they are factors
    for y in range( 2, x ):
        y_is_factor_of_x = is_factor( x, y )

        # y_is_factor_of_x is already a boolean value, so you don't need to include "== True" if you don't want to
        if ( y_is_factor_of_x == True ):
            result = False
            # Could just return False here, since we already know the answer now
        else:
            # Don't change anything if you don't find a factor
            pass

    return result