71116 ÷ 6 = 11852 R4
Alright, let's work through the division of 71116 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 6

Step 2:
6 goes into 11 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 6 from 11 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 6

Step 3:
6 goes into 51 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 118
Subtract 48 from 51 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 6

Step 4:
6 goes into 31 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 1185
Subtract 30 from 31 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 5:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 11852
Subtract 12 from 16 to get 4.

The final result is 11852 with a remainder of 4.