9585 ÷ 66 
Our goal is to divide 9585 by 66.

Step 1:
The number 66 fits into 9 0 times, leaving a remainder of 9.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Fetch the next digit (5) from the dividend, attach it to 9 and continue: 95 / 66

Let's proceed to step 2:
The number 66 fits into 95 1 times, leaving a remainder of 29.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 66 from 95 and we're left with 29.
Take the next digit (8) from the dividend and append it to 29, then repeat: 298 / 66

Let's proceed to step 3:
66 goes into 298 4 times with a remainder of 34.
Use 4 as the next digit of our solution. 
Result so far: 14.0
Subtracting 264 from 298 leaves us with 34.
Grab the next digit (5) from the dividend, add it to 34, then carry on: 345 / 66

On to step 4:
66 can be fit into 345 5 times, resulting in a remainder of 15.
The next digit of our result is 5. 
Result so far: 145.0
If we take 330 away from 345, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 5:
66 can be fit into 150 2 times, resulting in a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 145.2
If we subtract 132 from 150, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 6:
66 can be fit into 180 2 times, resulting in a remainder of 48.
Use 2 as the next digit of our solution. 
Result so far: 145.22
Deduct 132 from 180 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Our division results in 145.22 with a remaining 0.048.