We're dividing 259234 by 25 
We're looking to find how many times 25 goes into 259234.

Advancing to step 1:
2 divided by 25 is 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 25

Let's proceed to step 2:
When dividing 25 by 25, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 25 from 25 to get 0.
Fetch the next digit (9) from the dividend, attach it to 0 and continue: 9 / 25

Step 3:
25 can be fit into 9 0 times, resulting in a remainder of 9.
The next digit of our result is 0. 
Result so far: 10.0
If we subtract 0 from 9, we get 9.
Grab the next digit (2) from the dividend, add it to 9, then carry on: 92 / 25

Advancing to step 4:
25 can be fit into 92 3 times, resulting in a remainder of 17.
Use 3 as the next digit of our solution. 
Result so far: 103.0
Subtract 75 from 92 to get 17.
Take the next digit (3) from the dividend and append it to 17, then repeat: 173 / 25

Moving on to step 5:
25 can be fit into 173 6 times, resulting in a remainder of 23.
The number 6 becomes the next digit in our result. 
Result so far: 1036.0
If we take 150 away from 173, we end up with 23.
Take the next digit (4) from the dividend and append it to 23, then repeat: 234 / 25

Let's proceed to step 6:
25 goes into 234 9 times with a remainder of 9.
The next digit of our result is 9. 
Result so far: 10369.0
Subtracting 225 from 234 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 7:
25 can be fit into 90 3 times, resulting in a remainder of 15.
Put 3 as the next digit of the answer. 
Result so far: 10369.3
Subtracting 75 from 90 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 8:
150 divided by 25 is 6 with a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 10369.36
Deduct 150 from 150 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 9:
25 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 10369.36
Subtracting 0 from 0 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.

Step 10:
0 divided by 25 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 10369.36
Subtracting 0 from 0 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.

The quotient of the division is 10369.36, and the remainder is 0.0.