85943 ÷ 8 = 10742 R7
Let's divide 85943 by 8.

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 (5) of the dividend behind the 0 and repeat the process: 5 / 8

Step 2:
8 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 5 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 8

Step 3:
8 goes into 59 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 107
Subtract 56 from 59 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: 1074
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: 10742
Subtract 16 from 23 to get 7.

The final result is 10742 with a remainder of 7.