Goodbye.
   "Goodbye" itself is actually one of the most formal ways to say goodbye to someone. Here are some situations in which "Goodbye" is appropriate:
   ---You've broken up with your partner. You're sad about it. You think that you may never see this person again.
   ---You're angry with a family member. You say this as you slam the door or hang up the phone.
   Farewell.
   This phrase is quite formal and very emotional-sounding. It also seems very final. It's the type of thing that two lovers in a movie might say if they're never going to see each other again. You probably won't use it often in daily life.
   Have a good day.
   Say "Have a good day" (or "Have a nice day," "Have a good evening," or "Have a good night") to someone that you're not very close with, like a coworker that you don't know well, an employee, a customer, or a friend of a friend.
   Take care.
   This phrase is still a little bit formal, but not quite as formal as "Have a good day." Use this when you're not going to see someone again for at least a week.
   Most of the time, we use one of these casual phrases when saying goodbye to someone in English.
   'Bye!
   "'Bye" is the most common way to say goodbye in English. You can say "'Bye" to anyone you know, from friends to coworkers to clients. It's common to say "'Bye" at the very end of a conversation, even after you've said some of the other phrases in this list. For example:
   A: See you later.
   B: OK, have a good one.
   A: You too. 'Bye.
   B: 'Bye.
   Bye bye!
   Little children say "Bye bye", and adults say it when speaking to children. When adults use "Bye bye" with each other, it can either sound childish or sometimes flirtatious.
   Later!
  "Later!" is a cool, casual way to say goodbye. Men often use "Later!" when speaking with each other. You often follow "Later!" with something like "man", "bro", "dude", or "dear“. Ex: Later, man.
   See you later. / Talk to you later.
  "See you later is not quite as casual as "Later!". You can use it with almost anyone. You say "See you later" when you're saying goodbye to someone in person. When you're talking to someone on the phone, you can say "Talk to you later" instead.
   Have a good one.
"Have a good one" means "Have a good day" or "Have a good week." You sound relaxed and friendly when you use it. However, there are people who get annoyed by it because they think that "Have a good day" is better.
   So long.
  "So long" isn't very common for actually saying "goodbye" to someone, but you may find it sometimes in news headlines and other places.
   All right then.
   This isn't a very common phrase, but some people in the Southern part of the U.S. use it. It's very casual, relaxed, and colloquial.