Can't Make This Update Work - Advice??

Hi - I'm in a situation with a very large table, and trying to run an update that, any way I've approached it so far, seems to be taking unnacceptably long to run. Table has about 20 million rows, looks something like this:

ID - int, identity
Type - varchar(50)
PurchaseNumber - varchar(50)
SalesAmount - Money

ID Type PurchaseNumber SalesAmount
1 A 3834AA38384 20.32$
2 B 3834AA38384 11837.32$
3 C 3834AA38384 666.32$
4 C 887DF88U01H 23423.32$
5 A 887DF88U01H 12.32$
6 B OI83999FH28 4747.1$
7 D 38438495985 9384.6
8 E 02939DDJJWI 22.22$
9 F 07939SDFDF2 33.33$

The goal of the update is to make the [Type] uniform across [PurchaseNumbers], according to the max sales amount. For each PurchaseNumber a, set the type = the type of the row that has the MAX salesAmount. If there is only one entry for PurchaseNumber, leave the type alone. Expected update after completion would look like this:

ID Type PurchaseNumber SalesAmount
1 B 3834AA38384 20.32$
2 B 3834AA38384 11837.32$
3 B 3834AA38384 666.32$
4 C 887DF88U01H 23423.32$
5 C 887DF88U01H 12.32$
6 B OI83999FH28 4747.1$
7 D 38438495985 9384.6
8 E 02939DDJJWI 22.22$
9 F 07939SDFDF2 33.33$

I got this out of a warehouse, and it definitely isn't normalized well. Was considering breaking down into a better model, but I'm not yet sure if that would make the update easier.

I've been approaching this with sub-queries (finding all the PurchaseNumbers with more then one entry, then the max sales purchase of that purchase Number, then the type of that purchase number and sales amount to update all of that purchase number) but this not only ends up a little messy, but also very slow.

The only other detail that may be important is that out of the 20 million total rows, about 19.5 million purchaseNumbers are unique. So, really, there are only about 500k rows I actually have to update.

I've thought of a few ways to make this work, but none of them seem fast and wanted to see if anyone had a pointer. Thanks!