561353 ÷ 6 
Our goal is to divide 561353 by 6.

Advancing to step 1:
6 can be fit into 5 0 times, resulting in a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 6

Going ahead to step 2:
56 divided by 6 is 9 with a remainder of 2.
The next digit of our result is 9. 
Result so far: 9.0
Deduct 54 from 56 and we're left with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 6

On to step 3:
6 goes into 21 3 times with a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 93.0
The remainder is 3 after subtracting 18 from 21.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Going ahead to step 4:
6 goes into 33 5 times with a remainder of 3.
The next digit of our result is 5. 
Result so far: 935.0
Subtract 30 from 33 to get 3.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 6

On to step 5:
When dividing 35 by 6, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 9355.0
Subtracting 30 from 35 leaves us with 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Let's proceed to step 6:
The number 6 fits into 53 8 times, leaving a remainder of 5.
Record the quotient 8 as the next digit in the result. 
Result so far: 93558.0
Subtract 48 from 53 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 7:
The number 6 fits into 50 8 times, leaving a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 93558.8
Subtract 48 from 50 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:
The number 6 fits into 20 3 times, leaving a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 93558.83
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 9:
If we divide 20 by 6, we get 3 and a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 93558.833
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.

The quotient of the division is 93558.833, and the remainder is 0.0002.