Although paying off your last debt may feel liberating, it will not necessarily improve your credit score. Worse, it may actually lower your score, which may seem counterintuitive.
Paying off your credit card helps reduce credit utilization because your balance accounts for a small percentage of your total credit limit.
However, if you close the recently paid-off account, you will lose the account's credit limit, and your other balances will now account for a larger percentage of the total.