66172 ÷ 8 = 8271 R4
Alright, let's work through the division of 66172 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 (6) of the dividend behind the 6 and repeat the process: 66 / 8

Step 2:
8 goes into 66 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 64 from 66 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 8

Step 3:
8 goes into 21 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 82
Subtract 16 from 21 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 8

Step 4:
8 goes into 57 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 827
Subtract 56 from 57 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 8

Step 5:
8 goes into 12 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 8271
Subtract 8 from 12 to get 4.

The final result is 8271 with a remainder of 4.