6171 ÷ 8 = 771 R3
Alright, let's work through the division of 6171 by 8 step by step.

Step 1:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 8

Step 2:
8 goes into 61 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 56 from 61 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 8

Step 3:
8 goes into 57 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 77
Subtract 56 from 57 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 8

Step 4:
8 goes into 11 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 771
Subtract 8 from 11 to get 3.

The final result is 771 with a remainder of 3.