We look at the division of 251566 by 25 
We want to divide 251566 by 25.

Step 1:
The number 25 fits into 2 0 times, leaving a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 25

Going ahead to step 2:
When dividing 25 by 25, we get 1 with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 25 away from 25, we end up with 0.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 25

Let's proceed to step 3:
25 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 10.0
Deduct 0 from 1 and we're left with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 25

Advancing to step 4:
25 goes into 15 0 times with a remainder of 15.
Use 0 as the next digit of our solution. 
Result so far: 100.0
If we subtract 0 from 15, we get 15.
Append the next digit (6) from the dividend to 15 and continue with: 156 / 25

Going ahead to step 5:
25 can be fit into 156 6 times, resulting in a remainder of 6.
The next digit of our result is 6. 
Result so far: 1006.0
The remainder is 6 after subtracting 150 from 156.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 25

Advancing to step 6:
When dividing 66 by 25, we get 2 with a remainder of 16.
The next digit of our result is 2. 
Result so far: 10062.0
If we subtract 50 from 66, 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.

Moving on to step 7:
When dividing 160 by 25, we get 6 with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 10062.6
Subtract 150 from 160 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.

Going ahead to step 8:
25 can be fit into 100 4 times, resulting in a remainder of 0.
Write down 4 as next digit of the result. 
Result so far: 10062.64
Deduct 100 from 100 and we're left 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.

Step 9:
When dividing 0 by 25, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 10062.64
Deduct 0 from 0 and we're left 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.

Moving on to step 10:
25 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 10062.64
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.

In conclusion, the division gives 10062.64 with a balance of 0.0.