We're dividing 577210 by 77 
We want to figure out the number of times 577210 can be divided by 77.

On to step 1:
77 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 77

Going ahead to step 2:
When dividing 57 by 77, we get 0 with a remainder of 57.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 57, we get 57.
Include the next digit (7) from the dividend after 57, then repeat: 577 / 77

On to step 3:
77 can be fit into 577 7 times, resulting in a remainder of 38.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we subtract 539 from 577, we get 38.
Take the next digit (2) from the dividend and append it to 38, then repeat: 382 / 77

Going ahead to step 4:
When dividing 382 by 77, we get 4 with a remainder of 74.
Put 4 as the next digit of the answer. 
Result so far: 74.0
Deduct 308 from 382 and we're left with 74.
Bring next digit (1) of the dividend behind the 74 and repeat the process: 741 / 77

Going ahead to step 5:
If we divide 741 by 77, we get 9 and a remainder of 48.
The next digit of our result is 9. 
Result so far: 749.0
If we take 693 away from 741, we end up with 48.
Grab the next digit (0) from the dividend, add it to 48, then carry on: 480 / 77

Let's proceed to step 6:
77 goes into 480 6 times with a remainder of 18.
Record the quotient 6 as the next digit in the result. 
Result so far: 7496.0
Subtracting 462 from 480 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 7:
180 divided by 77 is 2 with a remainder of 26.
Put 2 as the next digit of the answer. 
Result so far: 7496.2
If we take 154 away from 180, we end up with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

On to step 8:
The number 77 fits into 260 3 times, leaving a remainder of 29.
Record the quotient 3 as the next digit in the result. 
Result so far: 7496.23
If we subtract 231 from 260, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 9:
290 divided by 77 is 3 with a remainder of 59.
The number 3 becomes the next digit in our result. 
Result so far: 7496.233
The remainder is 59 after subtracting 231 from 290.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

In conclusion, the division gives 7496.233 with a balance of 0.0059.