We look at the division of 553886 by 71 
Our goal is to divide 553886 by 71.

On to step 1:
71 can be fit into 5 0 times, resulting in a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 71

Let's proceed to step 2:
When dividing 55 by 71, we get 0 with a remainder of 55.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 55 leaves us with 55.
Fetch the next digit (3) from the dividend, attach it to 55 and continue: 553 / 71

On to step 3:
The number 71 fits into 553 7 times, leaving a remainder of 56.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Deduct 497 from 553 and we're left with 56.
Fetch the next digit (8) from the dividend, attach it to 56 and continue: 568 / 71

Let's proceed to step 4:
The number 71 fits into 568 8 times, leaving a remainder of 0.
Record the quotient 8 as the next digit in the result. 
Result so far: 78.0
Deduct 568 from 568 and we're left with 0.
Append the next digit (8) from the dividend to 0 and continue with: 8 / 71

Moving on to step 5:
The number 71 fits into 8 0 times, leaving a remainder of 8.
The next digit of our result is 0. 
Result so far: 780.0
Subtract 0 from 8 to get 8.
Fetch the next digit (6) from the dividend, attach it to 8 and continue: 86 / 71

On to step 6:
When dividing 86 by 71, we get 1 with a remainder of 15.
The next digit of our result is 1. 
Result so far: 7801.0
The remainder is 15 after subtracting 71 from 86.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 7:
When dividing 150 by 71, we get 2 with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 7801.2
Subtracting 142 from 150 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 8:
If we divide 80 by 71, we get 1 and a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 7801.21
Deduct 71 from 80 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:
The number 71 fits into 90 1 times, leaving a remainder of 19.
The next digit of our result is 1. 
Result so far: 7801.211
Subtracting 71 from 90 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

After the division, we end up with 7801.211 and a remainder of 0.0019.