66599 ÷ 6 
Our goal is to divide 66599 by 6.

Let's proceed to step 1:
If we divide 6 by 6, we get 1 and a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 0 after subtracting 6 from 6.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 6

Step 2:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 11.0
Deduct 6 from 6 and we're left with 0.
Grab the next digit (5) from the dividend, add it to 0, then carry on: 5 / 6

On to step 3:
5 divided by 6 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 110.0
Subtract 0 from 5 to get 5.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 6

Step 4:
59 divided by 6 is 9 with a remainder of 5.
The next digit of our result is 9. 
Result so far: 1109.0
If we take 54 away from 59, we end up with 5.
Fetch the next digit (9) from the dividend, attach it to 5 and continue: 59 / 6

Advancing to step 5:
59 divided by 6 is 9 with a remainder of 5.
Record the quotient 9 as the next digit in the result. 
Result so far: 11099.0
If we take 54 away from 59, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 6:
When dividing 50 by 6, we get 8 with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 11099.8
If we subtract 48 from 50, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
6 can be fit into 20 3 times, resulting in a remainder of 2.
The next digit of our result is 3. 
Result so far: 11099.83
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
6 goes into 20 3 times with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 11099.833
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 11099.833, and the remainder is 0.0002.