11516 ÷ 8 = 1439 R4
Alright, let's work through the division of 11516 by 8 step by step.

Step 1:
8 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 8

Step 2:
8 goes into 11 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 11 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 8

Step 3:
8 goes into 35 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 32 from 35 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 8

Step 4:
8 goes into 31 3 times with a remainder of 7.
Write down 3 as next digit of of the result. 
Result so far: 143
Subtract 24 from 31 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: 1439
Subtract 72 from 76 to get 4.

The final result is 1439 with a remainder of 4.