577257 ÷ 21 
We're looking to find how many times 21 goes into 577257.

On to step 1:
When dividing 5 by 21, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Include the next digit (7) from the dividend after 5, then repeat: 57 / 21

Let's proceed to step 2:
If we divide 57 by 21, we get 2 and a remainder of 15.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we subtract 42 from 57, we get 15.
Bring next digit (7) of the dividend behind the 15 and repeat the process: 157 / 21

Going ahead to step 3:
The number 21 fits into 157 7 times, leaving a remainder of 10.
Use 7 as the next digit of our solution. 
Result so far: 27.0
Deduct 147 from 157 and we're left with 10.
Append the next digit (2) from the dividend to 10 and continue with: 102 / 21

Going ahead to step 4:
21 can be fit into 102 4 times, resulting in a remainder of 18.
Put 4 as the next digit of the answer. 
Result so far: 274.0
Deduct 84 from 102 and we're left with 18.
Bring next digit (5) of the dividend behind the 18 and repeat the process: 185 / 21

On to step 5:
185 divided by 21 is 8 with a remainder of 17.
The next digit of our result is 8. 
Result so far: 2748.0
If we subtract 168 from 185, we get 17.
Bring next digit (7) of the dividend behind the 17 and repeat the process: 177 / 21

Going ahead to step 6:
If we divide 177 by 21, we get 8 and a remainder of 9.
Put 8 as the next digit of the answer. 
Result so far: 27488.0
If we subtract 168 from 177, 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.

Advancing to step 7:
90 divided by 21 is 4 with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 27488.4
The remainder is 6 after subtracting 84 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 8:
60 divided by 21 is 2 with a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 27488.42
If we subtract 42 from 60, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 9:
21 goes into 180 8 times with a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 27488.428
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 10:
If we divide 120 by 21, we get 5 and a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 27488.4285
The remainder is 15 after subtracting 105 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 11:
21 can be fit into 150 7 times, resulting in a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 27488.42857
Subtract 147 from 150 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 12:
When dividing 30 by 21, we get 1 with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 27488.428571
If we subtract 21 from 30, 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 13:
The number 21 fits into 90 4 times, leaving a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 27488.4285714
If we take 84 away from 90, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 14:
The number 21 fits into 60 2 times, leaving a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 27488.42857142
Subtract 42 from 60 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

In conclusion, the division gives 27488.42857142 with a balance of 1.8e-08.