Federal IDs don't have letters in them. You might be looking at the CUSIP, a stock ID number.
Make sure you are looking in the correct place on the 1099-DIV. The FEIN is usually in the header of the form, below the address.
An internet search showed the following:
For all nonretirement brokerage accounts, Vanguard Marketing Corporation (taxpayer identification number
23-2019846
) is the payer for all transactions on your Tax Information Statement or Form
1099
-MISC.