Even if you don't know about modulo, or (floor) division, you could subtract in a loop and see if you reach zero. Obviously not a good approach, but would demonstrate the kind of basic problem solving skill and ability to "write any working code at all" that this sort of thing is supposed to screen for.

You could improve that and still avoid any division or modulus by simply keeping track of when the "next fizz" and "next buzz" should occur. (And output "fizzbuzz" when those numbers are the same and you reach them.)

Yeah I've interviewed people who didn't.