86743 ÷ 8 = 10842 R7
Alright, let's work through the division of 86743 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 (7) of the dividend behind the 6 and repeat the process: 67 / 8

Step 3:
8 goes into 67 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 108
Subtract 64 from 67 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 8

Step 4:
8 goes into 34 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 1084
Subtract 32 from 34 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 8

Step 5:
8 goes into 23 2 times with a remainder of 7.
Write down 2 as next digit of of the result. 
Result so far: 10842
Subtract 16 from 23 to get 7.

The final result is 10842 with a remainder of 7.