817 ÷ 7 = 116 R5
Alright, let's work through the division of 817 by 7 step by step.

Step 1:
7 goes into 8 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 8 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 7

Step 2:
7 goes into 11 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 7 from 11 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 7

Step 3:
7 goes into 47 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 116
Subtract 42 from 47 to get 5.

The final result is 116 with a remainder of 5.