82665 ÷ 7 = 11809 R2
Alright, let's work through the division of 82665 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 (2) of the dividend behind the 1 and repeat the process: 12 / 7

Step 2:
7 goes into 12 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 7 from 12 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 7

Step 3:
7 goes into 56 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 118
Subtract 56 from 56 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 7

Step 4:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 1180
Subtract 0 from 6 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 7

Step 5:
7 goes into 65 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 11809
Subtract 63 from 65 to get 2.

The final result is 11809 with a remainder of 2.