96585 ÷ 7 = 13797 R6
Alright, let's work through the division of 96585 by 7 step by step.

Step 1:
7 goes into 9 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 9 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 7

Step 2:
7 goes into 26 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 21 from 26 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 7

Step 3:
7 goes into 55 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 137
Subtract 49 from 55 to get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 7

Step 4:
7 goes into 68 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 1379
Subtract 63 from 68 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 7

Step 5:
7 goes into 55 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 13797
Subtract 49 from 55 to get 6.

The final result is 13797 with a remainder of 6.