We're dividing 635688 by 11 
We want to figure out the number of times 635688 can be divided by 11.

On to step 1:
6 divided by 11 is 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 11

Advancing to step 2:
11 can be fit into 63 5 times, resulting in a remainder of 8.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtract 55 from 63 to get 8.
Fetch the next digit (5) from the dividend, attach it to 8 and continue: 85 / 11

On to step 3:
When dividing 85 by 11, we get 7 with a remainder of 8.
Write down 7 as next digit of the result. 
Result so far: 57.0
The remainder is 8 after subtracting 77 from 85.
Fetch the next digit (6) from the dividend, attach it to 8 and continue: 86 / 11

On to step 4:
If we divide 86 by 11, we get 7 and a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 577.0
If we take 77 away from 86, we end up with 9.
Bring next digit (8) of the dividend behind the 9 and repeat the process: 98 / 11

Advancing to step 5:
When dividing 98 by 11, we get 8 with a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 5778.0
The remainder is 10 after subtracting 88 from 98.
Fetch the next digit (8) from the dividend, attach it to 10 and continue: 108 / 11

Going ahead to step 6:
If we divide 108 by 11, we get 9 and a remainder of 9.
The number 9 becomes the next digit in our result. 
Result so far: 57789.0
If we subtract 99 from 108, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 7:
The number 11 fits into 90 8 times, leaving a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 57789.8
The remainder is 2 after subtracting 88 from 90.
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 8:
11 goes into 20 1 times with a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 57789.81
Deduct 11 from 20 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
11 can be fit into 90 8 times, resulting in a remainder of 2.
The next digit of our result is 8. 
Result so far: 57789.818
If we take 88 away from 90, 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.

Going ahead to step 10:
11 goes into 20 1 times with a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 57789.8181
Subtracting 11 from 20 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 11:
90 divided by 11 is 8 with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 57789.81818
If we take 88 away from 90, 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.

Going ahead to step 12:
11 goes into 20 1 times with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 57789.818181
Subtracting 11 from 20 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 13:
The number 11 fits into 90 8 times, leaving a remainder of 2.
The next digit of our result is 8. 
Result so far: 57789.8181818
The remainder is 2 after subtracting 88 from 90.
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 14:
11 goes into 20 1 times with a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 57789.81818181
Subtract 11 from 20 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

After the division, we end up with 57789.81818181 and a remainder of 9e-09.