Prime factors in 25 lines or less

[Antoni Gual]

Neuro's entry takes ages to factorize 2123456783, it issues a 7 at the start then it stands for a while.
I tried to modify it to make it faster, by not checking 2 and 3 multiples and stopping when the factor is equal to the square root of the remainder. Here is the result, 25 lines at all.

Code:

declare sub checkf(k&)
dim shared x&
do
  print
    INPUT "enter a number to factorize[0 to end] : ", x&
    if x&=0 then exit do
    PRINT "the prime factors are:";
    checkf(2)
    checkf(3)
    a&=2
    k& = 3 + a&
    WHILE k& <=int(sqr(x&))
      checkf(k&)
      k& = k& + a&
      a&=6&-a&
    WEND
    if x&>1 then print x&;
loop
PRINT "Ended"
sub checkf(k&)
WHILE x& MOD k& = 0
  x& = x& \ k&
  PRINT k&;
WEND
end sub