We're dividing 636669 by 55 
We want to divide 636669 by 55.

On to step 1:
If we divide 6 by 55, we get 0 and a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 55

Going ahead to step 2:
If we divide 63 by 55, we get 1 and a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 55 from 63 leaves us with 8.
Bring next digit (6) of the dividend behind the 8 and repeat the process: 86 / 55

Step 3:
86 divided by 55 is 1 with a remainder of 31.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
If we take 55 away from 86, we end up with 31.
Fetch the next digit (6) from the dividend, attach it to 31 and continue: 316 / 55

Moving on to step 4:
316 divided by 55 is 5 with a remainder of 41.
Put 5 as the next digit of the answer. 
Result so far: 115.0
The remainder is 41 after subtracting 275 from 316.
Append the next digit (6) from the dividend to 41 and continue with: 416 / 55

Moving on to step 5:
If we divide 416 by 55, we get 7 and a remainder of 31.
The number 7 becomes the next digit in our result. 
Result so far: 1157.0
Subtract 385 from 416 to get 31.
Grab the next digit (9) from the dividend, add it to 31, then carry on: 319 / 55

Step 6:
The number 55 fits into 319 5 times, leaving a remainder of 44.
The next digit of our result is 5. 
Result so far: 11575.0
Subtracting 275 from 319 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 7:
The number 55 fits into 440 8 times, leaving a remainder of 0.
Write down 8 as next digit of the result. 
Result so far: 11575.8
Subtracting 440 from 440 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
When dividing 0 by 55, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 11575.8
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 9:
If we divide 0 by 55, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 11575.8
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 11575.8, and the remainder is 0.0.