We're dividing 577255 by 9 
We want to figure out the number of times 577255 can be divided by 9.

Going ahead to step 1:
5 divided by 9 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (7) from the dividend after 5, then repeat: 57 / 9

Moving on to step 2:
57 divided by 9 is 6 with a remainder of 3.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we take 54 away from 57, we end up with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 9

Advancing to step 3:
37 divided by 9 is 4 with a remainder of 1.
Use 4 as the next digit of our solution. 
Result so far: 64.0
The remainder is 1 after subtracting 36 from 37.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 9

Moving on to step 4:
12 divided by 9 is 1 with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 641.0
If we subtract 9 from 12, we get 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 9

Moving on to step 5:
The number 9 fits into 35 3 times, leaving a remainder of 8.
Put 3 as the next digit of the answer. 
Result so far: 6413.0
The remainder is 8 after subtracting 27 from 35.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 9

Let's proceed to step 6:
When dividing 85 by 9, we get 9 with a remainder of 4.
The next digit of our result is 9. 
Result so far: 64139.0
If we take 81 away from 85, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
9 goes into 40 4 times with a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 64139.4
The remainder is 4 after subtracting 36 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
9 goes into 40 4 times with a remainder of 4.
The next digit of our result is 4. 
Result so far: 64139.44
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 64139.44, and the remainder is 0.004.