We look at the division of 585636 by 25 
We want to figure out the number of times 585636 can be divided by 25.

Step 1:
25 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 25

Moving on to step 2:
25 goes into 58 2 times with a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Deduct 50 from 58 and we're left with 8.
Bring next digit (5) of the dividend behind the 8 and repeat the process: 85 / 25

On to step 3:
25 goes into 85 3 times with a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 23.0
Deduct 75 from 85 and we're left with 10.
Append the next digit (6) from the dividend to 10 and continue with: 106 / 25

Moving on to step 4:
If we divide 106 by 25, we get 4 and a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 234.0
Deduct 100 from 106 and we're left with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 25

Step 5:
63 divided by 25 is 2 with a remainder of 13.
Put 2 as the next digit of the answer. 
Result so far: 2342.0
If we subtract 50 from 63, we get 13.
Include the next digit (6) from the dividend after 13, then repeat: 136 / 25

Advancing to step 6:
136 divided by 25 is 5 with a remainder of 11.
The number 5 becomes the next digit in our result. 
Result so far: 23425.0
The remainder is 11 after subtracting 125 from 136.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 7:
110 divided by 25 is 4 with a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 23425.4
Subtract 100 from 110 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
If we divide 100 by 25, we get 4 and a remainder of 0.
Record the quotient 4 as the next digit in the result. 
Result so far: 23425.44
Subtracting 100 from 100 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 23425.44 with a balance of 0.0.