We look at the division of 877259 by 25 
We're looking to find how many times 25 goes into 877259.

Step 1:
25 goes into 8 0 times with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Grab the next digit (7) from the dividend, add it to 8, then carry on: 87 / 25

Moving on to step 2:
25 goes into 87 3 times with a remainder of 12.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we take 75 away from 87, we end up with 12.
Append the next digit (7) from the dividend to 12 and continue with: 127 / 25

Let's proceed to step 3:
When dividing 127 by 25, we get 5 with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 35.0
Subtract 125 from 127 to get 2.
Grab the next digit (2) from the dividend, add it to 2, then carry on: 22 / 25

Moving on to step 4:
When dividing 22 by 25, we get 0 with a remainder of 22.
Record the quotient 0 as the next digit in the result. 
Result so far: 350.0
Subtract 0 from 22 to get 22.
Append the next digit (5) from the dividend to 22 and continue with: 225 / 25

Advancing to step 5:
25 can be fit into 225 9 times, resulting in a remainder of 0.
Record the quotient 9 as the next digit in the result. 
Result so far: 3509.0
Subtract 225 from 225 to get 0.
Grab the next digit (9) from the dividend, add it to 0, then carry on: 9 / 25

On to step 6:
When dividing 9 by 25, we get 0 with a remainder of 9.
The next digit of our result is 0. 
Result so far: 35090.0
Deduct 0 from 9 and we're left 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.

Advancing to step 7:
The number 25 fits into 90 3 times, leaving a remainder of 15.
The number 3 becomes the next digit in our result. 
Result so far: 35090.3
If we take 75 away from 90, we end up 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.

Step 8:
If we divide 150 by 25, we get 6 and a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 35090.36
Subtract 150 from 150 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.

On to step 9:
If we divide 0 by 25, we get 0 and a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 35090.36
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.

On to step 10:
When dividing 0 by 25, we get 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 35090.36
If we take 0 away from 0, 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.

Our division results in 35090.36 with a remaining 0.0.