clean and seal a concrete floor

I have a 22x60 foot concrete slab foundation that will serve as the floor for our house (radiant heat). We had originally intended to stain it, but think cleaning and sealing will give us the look we want.
Looking on the web, I see tons of products for cleaning concrete, but most appear to be for greasy garage floors. Our floor is just dirty with lots of dried drywall compound drops, but that's about it. Estimates to clean and seal from one company thus far was $2300 - they said they would use acids and special cleaners. No way am I going to pay that.
Do you think soap and water will do the trick? Do I need a pressure washer or some kind of special equipment to clean the floor? Any thoughts would be apprecaited.

Only you know what is on the floor. You can probably get as clean as you want to be with soap and water. You might consider borrowing or renting a floor buffer and some scrub pads. You can stay with the janitorial supply end of the world for floor finish as well.
(top posted for your convenience) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Keep the whole world singing . . . . DanG (remove the sevens) snipped-for-privacy@7cox.net
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You slab is 22x60 feet i.e. approx 124 m2. (Sorry, I am a metric frog :-) 2300 USD for that is 18.50 USD per m2. For a simple cleaning, it is way too high BUT you talk about "clean and seal" What do you mean by "seal". Is it applying after cleaning a concrete flooring coating? If yes, which type? The are hundreds with price ratio from 1 to 10! If your contractor offer includes a coating, it looks rather cheap to me. Cheers Daniel Note; If you have left-over of drywall compounds on that slab, soap and water won't do. You need a mechanical cleaning: blasting, grinding, etc...

Daniel - I have no idea what you just said, but thanks for saying it.

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Sorry, it's a French guy who is writing on a technical topic you are not familiar with. So, 2 handicaps: Mine (Language) + yours (Technicalities). On behalf of the world globalisation trend, let's try again :-)
You have a concrete floor slab. It is a bit dirty (Drywall compounds), probably dusty (By nature, concrete is generating dust) and also probably of an un-even grayish colour (Arrgh, how you say in the US, grey or gray??).
You want to clean it. Water and soap won't do the job for the drywall compound and any other construction chemical. You need a powered tool with a grinding disk or similar to remove all that, then only you can wash with water and soap. You can rent those tools, as mentioned by another poster.
Now, your concrete is clean. Good. No, not good as it won't last. Your floor will keep on generating dust and getting easily stained by any liquid you may spill (The worst are Italians: expresso coffee and tomate paste...). You may also dislike its colour(s).
So you have to paint it (Seal it): No more dust, easy to clean, colour of your choice and taste. You even have colourless paints if you like the concrete colour. There you have a big big choice. So many products. The choice is all on the type of use (Garage or living room? not the same usage conditions) and the durability you expect. (1 year? 5?,10?) You will find easily a lot of epoxy-based paints. It's OK but rather easy to scratch, and one scratch in epoxy = one black line in few weeks. Polyurethane-based paints are usually stronger and last longer.
Last important thing: It is a foundation slab, so there is a possibility that water comes up through your slab by capillarity. If it is the case, expect the paint to peel off. Concrete floor treatments that resist water rising up are available but *not* cheap.
Ready to try again if some stuff above is still not clear to you. Cheers Daniel

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Daniel - thanks for the clarification. I actually got a few scrub brushes and some detergent and cleaned the floor last night, all the drywall compound came right up with no problem. We're going to seal it this weekend with a readily available concrete sealer. Thanks again!

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Are we talking about gypsum drywall? Is French drywall compound different than US? Water and a little scrubbing is all you need and with a high pressure wash it goes much faster.

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No, not French, I am working in Asia. What they use here seems different from what is used in the US. When it's on concrete, one need mechancial grinding to get rid of it. Usually, the drywall contractor protects all the floor with a PE Sheet. It's not pure gypsum. When dry, the stuff is keeping some flexibility, so I guess that there are some polymers or resins in it, hence the "sticky" effect.
Amazing that at time of "globalisation", construction practices keep on being so different from a part of the world to the other. I have seen in this NG several US posts describing stuff I have never seen (30 years in the trade all over Europe, Middle East and Asia)!
Cheers Daniel

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Just ask the housecleaning people. They have to clean the bathrooms and its fixtures of drywall compound after a new construction. What you may find more difficult to remove is tile caulking or drywall compound with additives. But even that just takes a putty knife.
Muriatic acid may be used on concrete slabs that have oil, grease, or paint in their pores to aid removal. Its quite dangerous unless the proper clothing and precautions are used, with plenty of water rinse.
The point being is you must remove as much non-native material in the concrete surface pores for the sealer to "take" properly. Otherwise, it will appear patchwork.