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Hi all, The craftsman motor in my riding mower is trash. I tried replacing the piston rings, which definitely was the problem, but it's starting to burn a lot of oil again. I'm going to just replace it at this point. The model of the B&S is 31P977-0635-E1. How can I find out what's compatible with that? Is it just bolt pattern and outside dimensions? Shaft length too maybe? Thanks for the help!!

The recommended replacement engine is a 331877-3036-G5 which superceded to a 33S877-0019-G1. If switching to another brand of engine then the mounting pattern should be the same since that is mostly standardized. Now the differences will be in exhaust which may need to be made customer or totally replaced as well as modifying the wiring to work with the original mower wiring system. And will need to match the crank diameter and be really close on the same length. 1/8" difference in length is close enough.

Thanks for the help. Would a 33S877-0001 be the essentially the same as a 33S877-0019-G1 Looks exactly the same just no muffler (which I wouldn't use anyway). Would the type mean the difference in it working in my mower or not?

Yes
Any 33 series will bolt up
The only difference you are likely to come across is the oil filter ( or not ) and the alternator .
If they are diferent and have different plugs, the old one will swap directly over .

I want to replace a 46 series opposed with this:

will it likely bolt up?

I guess the muffler may be an issue but the shafts seem quite close in size.