We're dividing 605666 by 25 
Our goal is to divide 605666 by 25.

On to step 1:
When dividing 6 by 25, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (0) from the dividend, attach it to 6 and continue: 60 / 25

Step 2:
25 can be fit into 60 2 times, resulting in a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Deduct 50 from 60 and we're left with 10.
Grab the next digit (5) from the dividend, add it to 10, then carry on: 105 / 25

Advancing to step 3:
105 divided by 25 is 4 with a remainder of 5.
The next digit of our result is 4. 
Result so far: 24.0
Subtracting 100 from 105 leaves us with 5.
Grab the next digit (6) from the dividend, add it to 5, then carry on: 56 / 25

Step 4:
If we divide 56 by 25, we get 2 and a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 242.0
Subtract 50 from 56 to get 6.
Fetch the next digit (6) from the dividend, attach it to 6 and continue: 66 / 25

Let's proceed to step 5:
When dividing 66 by 25, we get 2 with a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 2422.0
If we subtract 50 from 66, we get 16.
Bring next digit (6) of the dividend behind the 16 and repeat the process: 166 / 25

Moving on to step 6:
25 can be fit into 166 6 times, resulting in a remainder of 16.
Put 6 as the next digit of the answer. 
Result so far: 24226.0
If we subtract 150 from 166, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 7:
If we divide 160 by 25, we get 6 and a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 24226.6
The remainder is 10 after subtracting 150 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
25 goes into 100 4 times with a remainder of 0.
Put 4 as the next digit of the answer. 
Result so far: 24226.64
If we subtract 100 from 100, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 9:
0 divided by 25 is 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 24226.64
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 10:
0 divided by 25 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 24226.64
The remainder is 0 after subtracting 0 from 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 24226.64 with a balance of 0.0.