59116 ÷ 8 = 7389 R4
Alright, let's work through the division of 59116 by 8 step by step.

Step 1:
8 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 8

Step 2:
8 goes into 59 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 56 from 59 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 8

Step 3:
8 goes into 31 3 times with a remainder of 7.
Write down 3 as next digit of of the result. 
Result so far: 73
Subtract 24 from 31 to get 7.
Bring next digit (1) of the dividend behind the 7 and repeat the process: 71 / 8

Step 4:
8 goes into 71 8 times with a remainder of 7.
Write down 8 as next digit of of the result. 
Result so far: 738
Subtract 64 from 71 to get 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 8

Step 5:
8 goes into 76 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 7389
Subtract 72 from 76 to get 4.

The final result is 7389 with a remainder of 4.