We're dividing 642877 by 25 
We're looking to find how many times 25 goes into 642877.

Advancing to step 1:
25 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 25

On to step 2:
25 can be fit into 64 2 times, resulting in a remainder of 14.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we take 50 away from 64, we end up with 14.
Append the next digit (2) from the dividend to 14 and continue with: 142 / 25

On to step 3:
The number 25 fits into 142 5 times, leaving a remainder of 17.
Record the quotient 5 as the next digit in the result. 
Result so far: 25.0
The remainder is 17 after subtracting 125 from 142.
Append the next digit (8) from the dividend to 17 and continue with: 178 / 25

Moving on to step 4:
178 divided by 25 is 7 with a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 257.0
The remainder is 3 after subtracting 175 from 178.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 25

Moving on to step 5:
The number 25 fits into 37 1 times, leaving a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 2571.0
The remainder is 12 after subtracting 25 from 37.
Append the next digit (7) from the dividend to 12 and continue with: 127 / 25

Moving on to step 6:
When dividing 127 by 25, we get 5 with a remainder of 2.
The next digit of our result is 5. 
Result so far: 25715.0
Deduct 125 from 127 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 7:
If we divide 20 by 25, we get 0 and a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 25715.0
If we subtract 0 from 20, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 8:
25 goes into 200 8 times with a remainder of 0.
The next digit of our result is 8. 
Result so far: 25715.08
The remainder is 0 after subtracting 200 from 200.
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:
The number 25 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 25715.08
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.

Let's proceed to step 10:
If we divide 0 by 25, we get 0 and a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 25715.08
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.

The final outcome is 25715.08, with a leftover of 0.0.