Ok from my storied past of washing home washing machine repair I can tell you that in most cases, the model number of the washer is completely useless. These days machines are assembled via a random collection of generic parts. On top of that, after a washer gets kind of old you can't find info on it.
You need to take the physical part off and look for a number on it. If that fails you need to do an image search for the part and find one that looks the same or close and that will give you the specific name and you can do some detective work from there.
I've worked on my own washer and grandma's several times over the years, the model number of the washers has never been helpful. Also sears will charge you triple what the part is worth. Buy washing machine parts NEW off of ebay. You'll get the exact same part for much less because you are essentially ordering it directly from China. (Yup all the replacement parts are made in China, unfortunately) The dog gears broke on Grandma's agitator a couple of months ago and I bought TWO kits off of Ebay for 1/3 the price of a single one via sears or your typical appliance shop.