81159 ÷ 8 = 10144 R7
Alright, let's work through the division of 81159 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 (1) of the dividend behind the 1 and repeat the process: 11 / 8

Step 3:
8 goes into 11 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 101
Subtract 8 from 11 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 8

Step 4:
8 goes into 35 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 1014
Subtract 32 from 35 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 8

Step 5:
8 goes into 39 4 times with a remainder of 7.
Write down 4 as next digit of of the result. 
Result so far: 10144
Subtract 32 from 39 to get 7.

The final result is 10144 with a remainder of 7.