Never give your personal phone number to someone if you are not comfortable doing so. It is always important to be polite, but you must consider your safety first.
If you are asked for your phone number and do not want to share it, you might say, “Thank you for asking, but I’m very busy right now.”
Never give someone a fake number. By doing so, you are giving them hope and may anger them when they discover it’s a false number. You wouldn’t want someone to do that to you, would you? Honesty is the best policy.