4971 ÷ 9 = 552 R3
Alright, let's work through the division of 4971 by 9 step by step.

Step 1:
9 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 9

Step 2:
9 goes into 49 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 45 from 49 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 9

Step 3:
9 goes into 47 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 55
Subtract 45 from 47 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 9

Step 4:
9 goes into 21 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 552
Subtract 18 from 21 to get 3.

The final result is 552 with a remainder of 3.