3.3.6 Where is the top-down design?

The top-down design starts with my assumption that ``someone else has already figured out how to find a factor $f$ of an integer $n > 1$ ''. This ``laziness'' actually works in my favor because it permits me to focus on the main logic of factoring a number. In other words, the ``top'' part of top-down is algorithm 1.

Once I traced algorithm 1, and am convinced that it works, I shift my attention to the assumed operation. Only at this time did I consider the logic of finding a prime factor $f$ of an integer $n > 1$ . Note that when I tried to figure out the logic of finding a prime factor of an integer, I don't need to worry about the logic of factoring a number anymore.