We're dividing 261569 by 25 
We want to divide 261569 by 25.

Let's proceed to step 1:
If we divide 2 by 25, we get 0 and a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 25

Going ahead to step 2:
25 goes into 26 1 times with a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 1 after subtracting 25 from 26.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 25

On to step 3:
The number 25 fits into 11 0 times, leaving a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 10.0
If we take 0 away from 11, we end up with 11.
Take the next digit (5) from the dividend and append it to 11, then repeat: 115 / 25

Let's proceed to step 4:
If we divide 115 by 25, we get 4 and a remainder of 15.
The number 4 becomes the next digit in our result. 
Result so far: 104.0
If we subtract 100 from 115, we get 15.
Bring next digit (6) of the dividend behind the 15 and repeat the process: 156 / 25

Going ahead to step 5:
The number 25 fits into 156 6 times, leaving a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 1046.0
The remainder is 6 after subtracting 150 from 156.
Fetch the next digit (9) from the dividend, attach it to 6 and continue: 69 / 25

Advancing to step 6:
The number 25 fits into 69 2 times, leaving a remainder of 19.
Record the quotient 2 as the next digit in the result. 
Result so far: 10462.0
Deduct 50 from 69 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Step 7:
If we divide 190 by 25, we get 7 and a remainder of 15.
The next digit of our result is 7. 
Result so far: 10462.7
The remainder is 15 after subtracting 175 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 8:
The number 25 fits into 150 6 times, leaving a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 10462.76
If we take 150 away from 150, we end up 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 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: 10462.76
Subtract 0 from 0 to 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.

Moving on to step 10:
When dividing 0 by 25, we get 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 10462.76
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.

The final outcome is 10462.76, with a leftover of 0.0.