9579 ÷ 6 = 1596 R3
Alright, let's work through the division of 9579 by 6 step by step.

Step 1:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 9 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 2:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 30 from 35 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 3:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 159
Subtract 54 from 57 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 6

Step 4:
6 goes into 39 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 1596
Subtract 36 from 39 to get 3.

The final result is 1596 with a remainder of 3.