555577 ÷ 65 
Our goal is to divide 555577 by 65.

Advancing to step 1:
5 divided by 65 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 65

Let's proceed to step 2:
The number 65 fits into 55 0 times, leaving 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.
Include the next digit (5) from the dividend after 55, then repeat: 555 / 65

Step 3:
When dividing 555 by 65, we get 8 with a remainder of 35.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Subtracting 520 from 555 leaves us with 35.
Take the next digit (5) from the dividend and append it to 35, then repeat: 355 / 65

Moving on to step 4:
355 divided by 65 is 5 with a remainder of 30.
The next digit of our result is 5. 
Result so far: 85.0
If we take 325 away from 355, we end up with 30.
Include the next digit (7) from the dividend after 30, then repeat: 307 / 65

Moving on to step 5:
65 goes into 307 4 times with a remainder of 47.
Put 4 as the next digit of the answer. 
Result so far: 854.0
Subtracting 260 from 307 leaves us with 47.
Grab the next digit (7) from the dividend, add it to 47, then carry on: 477 / 65

Going ahead to step 6:
477 divided by 65 is 7 with a remainder of 22.
Put 7 as the next digit of the answer. 
Result so far: 8547.0
If we take 455 away from 477, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 7:
If we divide 220 by 65, we get 3 and a remainder of 25.
Write down 3 as next digit of the result. 
Result so far: 8547.3
Subtracting 195 from 220 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 8:
250 divided by 65 is 3 with a remainder of 55.
The next digit of our result is 3. 
Result so far: 8547.33
The remainder is 55 after subtracting 195 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Our division results in 8547.33 with a remaining 0.055.