How to sign out of iCloud

The iCloud account that my iPad currently uses has a different Apple ID than the one I currently use. I never really had an issue with the notifications of verifying that Apple ID, as it would pop up like once or twice a day. However, when I upgraded to iOS 10.0.2, I was bombarded with iCloud notifications, asking me to verify the old Apple ID every minute or so. I tried to change my email to match the old one and turn off the iCloud. However, I cannot gain access to that email as it was hacked. The constant notifications every minute is making my iPad almost unusable. I want to know what to do next so that I can just turn off iCloud. Thanks in advance!