What happens if you reverse the two original numbers?
Try starting with $2, 8$ instead of $8, 2$.

What happens if you keep one of the starting numbers constant and only change the other?

It might be faster to use a spreadsheet or to write a short program to help you identify the limiting value (the value you get if you continue this process indefinitely).

Keep a record of your results.
Share your results.
Test out your ideas.