We look at the division of 556305 by 88 
Our goal is to divide 556305 by 88.

Moving on to step 1:
The number 88 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 88

Going ahead to step 2:
When dividing 55 by 88, we get 0 with a remainder of 55.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Grab the next digit (6) from the dividend, add it to 55, then carry on: 556 / 88

Let's proceed to step 3:
88 goes into 556 6 times with a remainder of 28.
The next digit of our result is 6. 
Result so far: 6.0
If we take 528 away from 556, we end up with 28.
Include the next digit (3) from the dividend after 28, then repeat: 283 / 88

Let's proceed to step 4:
When dividing 283 by 88, we get 3 with a remainder of 19.
Use 3 as the next digit of our solution. 
Result so far: 63.0
Subtract 264 from 283 to get 19.
Take the next digit (0) from the dividend and append it to 19, then repeat: 190 / 88

Moving on to step 5:
If we divide 190 by 88, we get 2 and a remainder of 14.
Write down 2 as next digit of the result. 
Result so far: 632.0
Subtracting 176 from 190 leaves us with 14.
Include the next digit (5) from the dividend after 14, then repeat: 145 / 88

Advancing to step 6:
If we divide 145 by 88, we get 1 and a remainder of 57.
Record the quotient 1 as the next digit in the result. 
Result so far: 6321.0
Deduct 88 from 145 and we're left with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Moving on to step 7:
88 goes into 570 6 times with a remainder of 42.
Write down 6 as next digit of the result. 
Result so far: 6321.6
If we subtract 528 from 570, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Step 8:
88 can be fit into 420 4 times, resulting in a remainder of 68.
The number 4 becomes the next digit in our result. 
Result so far: 6321.64
The remainder is 68 after subtracting 352 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Advancing to step 9:
When dividing 680 by 88, we get 7 with a remainder of 64.
Write down 7 as next digit of the result. 
Result so far: 6321.647
Deduct 616 from 680 and we're left with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Going ahead to step 10:
When dividing 640 by 88, we get 7 with a remainder of 24.
The number 7 becomes the next digit in our result. 
Result so far: 6321.6477
If we subtract 616 from 640, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The quotient of the division is 6321.6477, and the remainder is 0.00024.