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

def is_factor( x, y ) :
    ''' Parameters x and y are integers. The function returns whether y is a
        factor of x.
    '''

    # compute remainder of x divided by y
    rem = x % y

    # check it out
    if ( rem == 0 ) :   # check whether remainder is 0
        result = True   # if it is, return value is True
    else: 
        result = False  # if it is not, return value is False

    # return determination
    return result

def is_prime( x ) :
    ''' Parameter x is an integer. The function returns whether x is prime;
        i.e., its only factors are 1 and itself.
    '''
    result = True # initialize it outside of the loop, only update it if you find a factor
    for i in range( 2, x ) :
        if ( is_factor(x, i) == True ) : # check if i is a factor of x, if it is then x is not prime by definition
            # we can use the is_factor() function to make our lives easier, this is part of why we use functions
            result = False # can't have an else here, because if i is not a factor of x that does not ensure prime
    return result

def are_relative_primes( x, y ) :
    ''' Parameters x and y are integers. The function returns whether x and
        y are relatively prime; i.e., whether y is not a factor of x and
        vice-versa.
    '''
    # there are three possibilities. x is a factor of y, y is a factor of x, or they are relatively prime
    if ( is_factor( x, y ) == True ) :
        result = False
    elif ( is_factor( y, x ) == True ) :
        result = False
    else :
        result = True
    return result