We're dividing 557882 by 89 
Let's see how many times 89 fits into 557882.

Going ahead to step 1:
If we divide 5 by 89, we get 0 and 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.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 89

Moving on to step 2:
89 goes into 55 0 times with a remainder of 55.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 55 leaves us with 55.
Grab the next digit (7) from the dividend, add it to 55, then carry on: 557 / 89

Let's proceed to step 3:
The number 89 fits into 557 6 times, leaving a remainder of 23.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we subtract 534 from 557, we get 23.
Append the next digit (8) from the dividend to 23 and continue with: 238 / 89

Moving on to step 4:
89 can be fit into 238 2 times, resulting in a remainder of 60.
The next digit of our result is 2. 
Result so far: 62.0
The remainder is 60 after subtracting 178 from 238.
Fetch the next digit (8) from the dividend, attach it to 60 and continue: 608 / 89

On to step 5:
The number 89 fits into 608 6 times, leaving a remainder of 74.
Record the quotient 6 as the next digit in the result. 
Result so far: 626.0
Deduct 534 from 608 and we're left with 74.
Include the next digit (2) from the dividend after 74, then repeat: 742 / 89

Step 6:
If we divide 742 by 89, we get 8 and a remainder of 30.
Put 8 as the next digit of the answer. 
Result so far: 6268.0
Deduct 712 from 742 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 7:
When dividing 300 by 89, we get 3 with a remainder of 33.
The number 3 becomes the next digit in our result. 
Result so far: 6268.3
Deduct 267 from 300 and we're left 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.

Step 8:
When dividing 330 by 89, we get 3 with a remainder of 63.
Record the quotient 3 as the next digit in the result. 
Result so far: 6268.33
Subtracting 267 from 330 leaves us with 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

The quotient of the division is 6268.33, and the remainder is 0.063.