We look at the division of 665626 by 63 
We're looking to find how many times 63 goes into 665626.

Step 1:
When dividing 6 by 63, we get 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Fetch the next digit (6) from the dividend, attach it to 6 and continue: 66 / 63

On to step 2:
When dividing 66 by 63, we get 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 63 from 66, we get 3.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 63

Let's proceed to step 3:
If we divide 35 by 63, we get 0 and a remainder of 35.
The next digit of our result is 0. 
Result so far: 10.0
If we take 0 away from 35, we end up with 35.
Fetch the next digit (6) from the dividend, attach it to 35 and continue: 356 / 63

Step 4:
63 can be fit into 356 5 times, resulting in a remainder of 41.
The next digit of our result is 5. 
Result so far: 105.0
Subtracting 315 from 356 leaves us with 41.
Fetch the next digit (2) from the dividend, attach it to 41 and continue: 412 / 63

Moving on to step 5:
63 can be fit into 412 6 times, resulting in a remainder of 34.
The number 6 becomes the next digit in our result. 
Result so far: 1056.0
If we take 378 away from 412, we end up with 34.
Include the next digit (6) from the dividend after 34, then repeat: 346 / 63

Going ahead to step 6:
63 can be fit into 346 5 times, resulting in a remainder of 31.
The next digit of our result is 5. 
Result so far: 10565.0
If we take 315 away from 346, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 7:
63 goes into 310 4 times with a remainder of 58.
Use 4 as the next digit of our solution. 
Result so far: 10565.4
Deduct 252 from 310 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

On to step 8:
If we divide 580 by 63, we get 9 and a remainder of 13.
Use 9 as the next digit of our solution. 
Result so far: 10565.49
Subtracting 567 from 580 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 9:
The number 63 fits into 130 2 times, leaving a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 10565.492
If we take 126 away from 130, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 10:
40 divided by 63 is 0 with a remainder of 40.
The next digit of our result is 0. 
Result so far: 10565.492
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 11:
If we divide 400 by 63, we get 6 and a remainder of 22.
The number 6 becomes the next digit in our result. 
Result so far: 10565.49206
If we subtract 378 from 400, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 12:
When dividing 220 by 63, we get 3 with a remainder of 31.
Put 3 as the next digit of the answer. 
Result so far: 10565.492063
If we take 189 away from 220, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Let's proceed to step 13:
When dividing 310 by 63, we get 4 with a remainder of 58.
The next digit of our result is 4. 
Result so far: 10565.4920634
Subtracting 252 from 310 leaves us with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Step 14:
The number 63 fits into 580 9 times, leaving a remainder of 13.
Put 9 as the next digit of the answer. 
Result so far: 10565.49206349
Subtracting 567 from 580 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The quotient of the division is 10565.49206349, and the remainder is 1.3e-08.