We're dividing 577128 by 61 
We want to figure out the number of times 577128 can be divided by 61.

Moving on to step 1:
5 divided by 61 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 61

On to step 2:
61 can be fit into 57 0 times, resulting in a remainder of 57.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 57 to get 57.
Take the next digit (7) from the dividend and append it to 57, then repeat: 577 / 61

Let's proceed to step 3:
If we divide 577 by 61, we get 9 and a remainder of 28.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
If we subtract 549 from 577, we get 28.
Append the next digit (1) from the dividend to 28 and continue with: 281 / 61

Advancing to step 4:
61 can be fit into 281 4 times, resulting in a remainder of 37.
Put 4 as the next digit of the answer. 
Result so far: 94.0
Subtracting 244 from 281 leaves us with 37.
Include the next digit (2) from the dividend after 37, then repeat: 372 / 61

Moving on to step 5:
372 divided by 61 is 6 with a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 946.0
Deduct 366 from 372 and we're left with 6.
Include the next digit (8) from the dividend after 6, then repeat: 68 / 61

Going ahead to step 6:
If we divide 68 by 61, we get 1 and a remainder of 7.
The next digit of our result is 1. 
Result so far: 9461.0
Subtract 61 from 68 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 7:
When dividing 70 by 61, we get 1 with a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 9461.1
If we subtract 61 from 70, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 8:
61 goes into 90 1 times with a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 9461.11
If we subtract 61 from 90, 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.

In conclusion, the division gives 9461.11 with a balance of 0.029.