Do a search for the particular model. When you see a grouping of websites in Google Products with a "compare prices" button, click that button. You'll see a list of sites. Scroll to the bottom of the page and you'll see the details, such as model number, UPC code, etc.
It's always possible that Google got the number from a merchant who had it wrong, so I'm getting my UPC numbers from the manufacturer.
I've done well with Google Products the past several years, and just this weekend added UPC codes to see if it might improve things.