81966 ÷ 9 = 9107 R3
Alright, let's work through the division of 81966 by 9 step by step.

Step 1:
9 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 8 to get 8.
Bring next digit (1) of the dividend behind the 8 and repeat the process: 81 / 9

Step 2:
9 goes into 81 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 81 from 81 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 9

Step 3:
9 goes into 9 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 91
Subtract 9 from 9 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 9

Step 4:
9 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 910
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 9

Step 5:
9 goes into 66 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 9107
Subtract 63 from 66 to get 3.

The final result is 9107 with a remainder of 3.