666561 ÷ 63 
We want to divide 666561 by 63.

Advancing to step 1:
When dividing 6 by 63, we get 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 63

Step 2:
63 goes into 66 1 times with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 63 from 66 to get 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 63

Step 3:
36 divided by 63 is 0 with a remainder of 36.
Write down 0 as next digit of the result. 
Result so far: 10.0
If we take 0 away from 36, we end up with 36.
Include the next digit (5) from the dividend after 36, then repeat: 365 / 63

Going ahead to step 4:
When dividing 365 by 63, we get 5 with a remainder of 50.
Use 5 as the next digit of our solution. 
Result so far: 105.0
If we take 315 away from 365, we end up with 50.
Grab the next digit (6) from the dividend, add it to 50, then carry on: 506 / 63

Let's proceed to step 5:
506 divided by 63 is 8 with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 1058.0
If we take 504 away from 506, we end up with 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 63

Advancing to step 6:
The number 63 fits into 21 0 times, leaving a remainder of 21.
Write down 0 as next digit of the result. 
Result so far: 10580.0
Subtract 0 from 21 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
63 can be fit into 210 3 times, resulting in a remainder of 21.
Use 3 as the next digit of our solution. 
Result so far: 10580.3
Deduct 189 from 210 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Going ahead to step 8:
If we divide 210 by 63, we get 3 and a remainder of 21.
Put 3 as the next digit of the answer. 
Result so far: 10580.33
Deduct 189 from 210 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

In conclusion, the division gives 10580.33 with a balance of 0.021.