81966 ÷ 8 = 10245 R6
Alright, let's work through the division of 81966 by 8 step by step.

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

Step 2:
8 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 8

Step 3:
8 goes into 19 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 16 from 19 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 8

Step 4:
8 goes into 36 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 1024
Subtract 32 from 36 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 8

Step 5:
8 goes into 46 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 10245
Subtract 40 from 46 to get 6.

The final result is 10245 with a remainder of 6.