I guess that I have more to learn (don't we always), I've always thought the x factor essentially meant that you multiplied the FSB times the x factor to get the processor speed. Told you it was probably a dumb question.... so can someone please explain to me how having the multiplier set at 3/2 or 1.5x (which equals 99.9 - effectively 100mhz) gets 233Mhz cpu speed (or 200Mhz for that matter)? My incorrect knowledge would have guessed 3/1 or 3x (effectively 200Mhz).

Go one level deeper and it makes sense.

The Socket 7 specification defined two pins for multiplier setting, BF0 and BF1. That gives 2^2=4 options. In the original Pentium those four options were mapped to 1.5x, 2.0x, 2.5x and 3.0x.
Then the P55C (Pentium MMX) came along. Intel wanted higher clock speeds, but the CPUs had to work on the same motherboards as the original Pentium. So they changed the mapping: they did not foresee using a 1.5x multiplier so the re-mapped it to 3.5x. That made the mapping 3.5x, 2.0x, 2.5x and 3.0x. So even if your board didn't mention Pentium MMX or 3.5x explicitly, you could just set the multiplier jumpers to "1.5x" and you got 3.5x.
AMD did the same thing later on with the K6-2/3 series of CPUs: at the time there were three multiplier pins offering 2^3=8 settings, from 2.0x-5.5x. However they wanted to be able to run at 400MHz on a 66MHz FSB so needed a 6x multiplier. They re-mapped the 2.0x setting to 6.0x in later K6-2 and all K6-3 CPUs.

I am aware of the 2.8v vs 3.3v MMX vs Classic voltage quandry, so I'm looking into coolers and such, but I note that for my processor this site lists a 'core voltage' of 2.8v but an I/O voltage of 3.3v:
https://www.cpu-world.com/sspec/SL/SL27S.html

What's the difference between core voltage and I/O voltage? I was going to assume that the I/O voltage means essentially 'what the CPU can handle vs what it needs' but you know what they say about assuming...

Back to Intel's Socket 7 spec here.

Originally CPUs ran at the same clock speed and the same voltage as the rest of the system. But advances in CPU core technology went faster than were possible on buses, so it became necessary to first run the CPU at a multiple of the bus speed, but those higher speeds needed smaller parts which ran at lower voltages. So it became necessary to run the CPU core at a lower voltage to the rest of the system. Socket 7 defined two voltage planes, Vcore and VIO. The first So7 CPUs (and motherboards!) ran both at the same level, but split voltage became a thing around the time the Pentium MMX came along. So the core runs at say 2.8V when the IO (the CPU bus that communicates with the motherboard chipset) still runs at 3.3V. The fact that I/O voltage is 3.3V does NOT mean you can run the core at that level. In the case of the (heavily over-engineered) Pentium MMX you can get away with it if sufficiently cooled, but you really should run Pentium MMX CPUs on a board with split voltage that lets you run the core at or near 2.8V as specified.

If your motherboard doesn't offer split voltage, you should look for a voltage interposer or another motherboard. Or run a Pentium classic that likes the single 3.3V levels.

Just to elaborate - the motherboard doesn't du anything with the multiplier besides telling the CPU which multiplier to choose. The actual multiplication is done inside the CPU, according to what the motherboard asks it to. This is why the 1.5->3.5 remapping works.

Can you find the ultimate retro link for your board?

If the board only supports single voltage your best option is a mmx overdrive or a k6-233

Running a pentium mmx at 3.3v is not ideal.

The correct setting for 233mmx is 1.5x 66mhz 100mhz that will translate in the cpu to 3.5x 66mhz 233mhz

There are also voltage interposers that will allow dual voltage operation allowing up to a k6-3+ 400mhz to be used. Or any cpu between.

Socket 5/7/SS7 (Voltage Interposer) Tweaker. (Released)

You may need bios mods
DIY Bios Modding guide Jan Steunebrink k6-2+/3+ 128gb

First of all, sorry it took a few days to get back to you all. Life has been busy. Your answers were very helpful in getting me to understand this, and also I find the esoteric history of these developments interesting. So I got more than I thought I would and that's awesome, and I greatly appreciate the answers.

Regarding my mobo, I'm working on two... sort of. I acquired an IBM 350 P100, which uses DIP switches instead of jumpers. It was working fine.. until suddenly it wasn't. I'll start a separate thread about that, but after troubleshooting I snagged another slightly newer board from an Aptiva. Unfortunately I don't have the riser and the riser is different than the original 350's board. Dumb, but there ya go, I'll put it aside and chalk it up to learning (I put an ebay search in to alert me for the correct riser based on a part number I got from another site that was noted on another post here). Either board is single voltage, the Aptiva's being one that juuuuuust predates the MMXs.

I've soldered bigger much older electronics but that skill level isn't enough to handle building one of those interposers - my other hobbies are restoring typewriters and vintage audio pre-1970, though I have repaired a power supply on a 1980s TA Royal Officemaster printer and will be doing so shortly on an IBM Correcting Quietwriter printer; both of those feature pretty large power supply boards and components, so I can handle those.

The other solution for the single voltage boards is I acquire one of the pentium overdrive kits Intel sold,which includes the stuff needed to deal with the voltages (and a fan).

Anyway, thanks for your answers, I'll address the stuff I'm trying to figure out on the 350's board in another thread.

EDIT: That is, I'll post about those issues on the 350's board once I'm sure the answers aren't elsewhere here. I know I can't be the only person who has dealt with what I am seeing, though I haven't found anything yet that quite matches it. 😁