We're dividing 557882 by 71 
We're looking to find how many times 71 goes into 557882.

Let's proceed to step 1:
If we divide 5 by 71, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 71

Going ahead to step 2:
55 divided by 71 is 0 with a remainder of 55.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Append the next digit (7) from the dividend to 55 and continue with: 557 / 71

Step 3:
When dividing 557 by 71, we get 7 with a remainder of 60.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtract 497 from 557 to get 60.
Include the next digit (8) from the dividend after 60, then repeat: 608 / 71

Moving on to step 4:
71 can be fit into 608 8 times, resulting in a remainder of 40.
Put 8 as the next digit of the answer. 
Result so far: 78.0
The remainder is 40 after subtracting 568 from 608.
Take the next digit (8) from the dividend and append it to 40, then repeat: 408 / 71

Step 5:
When dividing 408 by 71, we get 5 with a remainder of 53.
Put 5 as the next digit of the answer. 
Result so far: 785.0
If we subtract 355 from 408, we get 53.
Bring next digit (2) of the dividend behind the 53 and repeat the process: 532 / 71

Going ahead to step 6:
71 can be fit into 532 7 times, resulting in a remainder of 35.
The next digit of our result is 7. 
Result so far: 7857.0
Subtracting 497 from 532 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 7:
The number 71 fits into 350 4 times, leaving a remainder of 66.
The number 4 becomes the next digit in our result. 
Result so far: 7857.4
Deduct 284 from 350 and we're left with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Moving on to step 8:
When dividing 660 by 71, we get 9 with a remainder of 21.
The number 9 becomes the next digit in our result. 
Result so far: 7857.49
Subtract 639 from 660 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 9:
When dividing 210 by 71, we get 2 with a remainder of 68.
Record the quotient 2 as the next digit in the result. 
Result so far: 7857.492
Deduct 142 from 210 and we're left with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

On to step 10:
680 divided by 71 is 9 with a remainder of 41.
The next digit of our result is 9. 
Result so far: 7857.4929
Subtracting 639 from 680 leaves us with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Let's proceed to step 11:
If we divide 410 by 71, we get 5 and a remainder of 55.
Record the quotient 5 as the next digit in the result. 
Result so far: 7857.49295
The remainder is 55 after subtracting 355 from 410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 12:
71 goes into 550 7 times with a remainder of 53.
The next digit of our result is 7. 
Result so far: 7857.492957
Subtract 497 from 550 to get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

On to step 13:
The number 71 fits into 530 7 times, leaving a remainder of 33.
The number 7 becomes the next digit in our result. 
Result so far: 7857.4929577
Subtracting 497 from 530 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

The quotient of the division is 7857.4929577, and the remainder is 3.3e-07.