We look at the division of 8553071 by 629 
We want to divide 8553071 by 629.

Going ahead to step 1:
629 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Grab the next digit (5) from the dividend, add it to 8, then carry on: 85 / 629

Advancing to step 2:
If we divide 85 by 629, we get 0 and a remainder of 85.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 85 to get 85.
Include the next digit (5) from the dividend after 85, then repeat: 855 / 629

Let's proceed to step 3:
629 can be fit into 855 1 times, resulting in a remainder of 226.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 629 from 855 and we're left with 226.
Grab the next digit (3) from the dividend, add it to 226, then carry on: 2263 / 629

Moving on to step 4:
When dividing 2263 by 629, we get 3 with a remainder of 376.
Write down 3 as next digit of the result. 
Result so far: 13.0
Subtracting 1887 from 2263 leaves us with 376.
Append the next digit (0) from the dividend to 376 and continue with: 3760 / 629

On to step 5:
3760 divided by 629 is 5 with a remainder of 615.
The number 5 becomes the next digit in our result. 
Result so far: 135.0
Subtracting 3145 from 3760 leaves us with 615.
Fetch the next digit (7) from the dividend, attach it to 615 and continue: 6157 / 629

On to step 6:
When dividing 6157 by 629, we get 9 with a remainder of 496.
Use 9 as the next digit of our solution. 
Result so far: 1359.0
Subtract 5661 from 6157 to get 496.
Grab the next digit (1) from the dividend, add it to 496, then carry on: 4961 / 629

Advancing to step 7:
4961 divided by 629 is 7 with a remainder of 558.
Put 7 as the next digit of the answer. 
Result so far: 13597.0
Deduct 4403 from 4961 and we're left with 558.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5580, and continue the process.

Going ahead to step 8:
The number 629 fits into 5580 8 times, leaving a remainder of 548.
Write down 8 as next digit of the result. 
Result so far: 13597.8
If we subtract 5032 from 5580, we get 548.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5480, and continue the process.

Step 9:
629 can be fit into 5480 8 times, resulting in a remainder of 448.
The next digit of our result is 8. 
Result so far: 13597.88
Deduct 5032 from 5480 and we're left with 448.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4480, and continue the process.

The quotient of the division is 13597.88, and the remainder is 0.448.