power supply - Using Linear Voltage Regulators in Series?

I'm trying to design a power supply circuit that can output four voltages from the same circuit using linear voltage regulators. I'm still learning a lot of this, and trying to stick to the LM7800 series for this application. The circuit currently uses the following regulators with a 15V input supply to produce four output voltages:

1. LM7812 straight to output 12V DC


2. LM7809 to output 9V DC


3. LM7805 input connected to LM7809 output for 5V DC (to try and avoid excessive heat output from the LM7805)



4. LM7810 on a 4kΩ+2kΩ voltage divider (if these values are too much, any ratio of ^R₁/_R2 = ²/₁ will work) to step down to 3.3V DC

To that effect, I have a few questions about the design of the circuit:

1. Is it a good idea to use the voltage output of one voltage regulator to power the input of another? I did read that the LM7800 series exhausts excess energy as heat, so I'm trying to avoid driving the LM7805 with the full 15V input.


2. If #1 is not a good idea, would it be possible to use a voltage divider before the input of the LM7805 instead?


3. Is there a voltage regulator in the LM7800 series that provides 3.3V directly instead of relying on a stepped-down LM7810? I did a quick search on Google for LM78033, but most of the results that I got were for defunct pages or for products that are no longer offered.

My primary circuit design constraint is simplicity. I'd like to make it compact enough, preferably using THT components, to fit on a PC board that can be turned into a DIP package for breadboard use.