86126 ÷ 8 = 10765 R6
Alright, let's work through the division of 86126 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 (6) of the dividend behind the 0 and repeat the process: 6 / 8

Step 2:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 6 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 8

Step 3:
8 goes into 61 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 107
Subtract 56 from 61 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 8

Step 4:
8 goes into 52 6 times with a remainder of 4.
Write down 6 as next digit of of the result. 
Result so far: 1076
Subtract 48 from 52 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: 10765
Subtract 40 from 46 to get 6.

The final result is 10765 with a remainder of 6.