Can't clear unread email badge after updating to iOS 7?

I've just updated my iPhone 5 to iOS 7 and now I have a badge on my Mail app icon showing 1344 unread messages. I've tried turning mail off, turning the phone off and back on and then turning mail back on; deleting and re-adding my account; and marking all the messages in the Mail app on my Mac unread, syncing, and marking them read again.
Does anyone know how to fix this without jailbreaking? It's driving me crazy.
Thanks!

Added (1). FOUND A SOLUTION FOR GMAIL - Please NO MORE ANSWERS.
Log into Gmail in your web browser. Using the advanced search, type some random text into the "does not contain" box (this needs to be something that no message in your inbox would ever contain. I just typed a bunch of random letters). Click on the select all checkbox in the corner, it will prompt you to select all messages that match your search. Click on that, then mark all as unread. Check for mail on your iPhone and the count should go down to zero.

I'm having a similar issue, however mine is that one of my email inboxes is now showing all 'read' messages. The other email inboxes are still only showing the notification for number of 'unread' messages. I've searched high and low in my Settings and can't figure out how to fix this issue. I want to only see 'unread' messages in All of my email inboxes.

Go to Settings / Mail
Choose the mail account with the issue
Turn mail Off and let it unload for a minute
Turn mail back On and those unreads should be gone

I currently have 12032 emails showing! Grrrrrrrr help?

1.open the email you are having issues with (i.e.showing incorrect number of unread messages). For whatever reason, I had about 14, 000.
2.select "edit" on top right hand corner
3.select "mark all" on bottom left
4.select "mark as read".

That worked for me.

1.open the email you are having issues with (i.e.showing incorrect number of unread messages). For whatever reason, I had about 14, 000.
2.select "edit" on top right hand corner
3.select "mark all" on bottom left
4.select "mark as read".

That worked for me.

(thanks! This worked perfectly)

Tried both fixes but after a while the count comes back. Tried deleting them also and they came back as well.

Go to mailbox having issues, hit edit, hit mark all, hit as read. I did this a few times along with flagging and unflagging and after about a minute it worked on ipad and same issue automatically resolved on phone

I got the red numbers cleared by going to Edit, Mark all as unread, Edit, Mark all as read, for each mailbox… Finally cleared it!

I have tried both fixes, off/on and mark unread/read. Both work only momentarily. In a couple of minutes the flags are back!

The only way I got the badges to disappear was to go to the Notification Center and select Mail and turn off the badges for the problem mailboxes.

Your additional details worked for me, did the same thing in gmail and now my phone shows 0. Doing some of the other things people recommended like editting and marking read did NOT work for me.