8177 ÷ 8 = 1022 R1
Alright, let's work through the division of 8177 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 (7) of the dividend behind the 1 and repeat the process: 17 / 8

Step 3:
8 goes into 17 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 16 from 17 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 8

Step 4:
8 goes into 17 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 1022
Subtract 16 from 17 to get 1.

The final result is 1022 with a remainder of 1.