The HostGator nameservers that you need to set your domain to are listed in the initial welcome setup email.
They will look like x.hostgator.com and y.hostgator.com. There are always a minimum of two nameservers needed since one is primary and one is secondary, incase the primary nameserver fails.
If you’ve lost the setup email, this information can also be accessed in your cPanel account, if you’re on a Shared hosting plan.
Once logged in, scroll down to your Account Information.
Under your package and IP address, you’ll see a row for Name Servers.
Simply copy these one at a time and enter in your domain registrar’s field for name servers.