I believe that would be a Carter Model N carburetor. You can google that then verify with the seller (or maybe an expert will jump in here). Here are a couple of starting points (they ain't cheap).
Good luck.

http://members.aol.com/pullingtractor/a1carb.htm

http://www.kohler-engine-parts.opeengines.com/index.php?main_page=product_info&products_id=1669

I have a correctuion on the number of the carb. It's G230500. That other number is not used by repair people I have learned, to be ignored. The 230500 was on top buried under gas film and dirt. Hope this helps anyone trying to help me. Thanks bruce

Contact the Troy-Bilt guru, Bill Rodgers (bilrodgers@yahoo.com), or call him @ Valley Power Products (he owns it) @ 800-609-5110. He stocks parts for these vintage tillers.

Thanks for info on Bill Rodgers. He has a brand new one in stock, a mere 200 bucks. But I may well have to do it that way. I am waiting to call another source that is supposed to be top notch rebuilt ones for 100 bucks. Thanks for all your input, and if anyone has a good idea here I am not buying till Wednesday 6-18, thanks again, Bruce

Brian Miller is a rebuilder and has them for sale most of the time.

Here is a link that might be useful: Brian Miller

Bruce, Take a look at eBay, NOW. There's a carb for a K181 and I believe the carb body is the same as K161. You could switch jets and all. I can't find that engine spec on Kohler's site but I have a Horse III with the K161T engine and it's a Kohler built carb. Hope you haven't bought, yet.
Good Luck! KK

Or get the identical one:

http://cgi.ebay.com/KOHLER-K161-ENGINE-CARBURETOR-CARB-AND-AIR-CLEANER_W0QQitemZ280237549695QQihZ018QQcategoryZ79670QQssPageNameZWDVWQQrdZ1QQcmdZViewItem

Thanks to you all who responded. I finally found several sites that had new carbs for 200 bucks plus shipping. Finally, only 100 miles from my home I found a dealer who had the precise carb, new in the box, shipping included for 150.30. A rebuilt one was 100 plus shipping, so I took the new one. That machine still looks as good as new, runs like a watch, and has many years left, well worth fixing it right

Hello, can anyone help me? I have a Troy Bilt 7HP kohler engine on the horse model Roto-tiller, spec# 282287J Ser#11136034 model K-161-T, I need all tune up specs, carb air/fuel mixture screw settings, plug gap, point gap, head bolt torque settings, and how to adjust the governor in conjunction with the throttle cable and what is the max RPM, I know it's a lot but I keep getting no response locally where I live and they all act anal. IT's a great tiller and has a lot of life left, Troy-Bilt needs to start making them like this again instead of the piece of crap they sell now, modern troybilts suck, I still say old school when they built everything the right way. Thanks Paul Here is my E-mail address ps13811@aol.com