We look at the division of 636503 by 25 
We want to divide 636503 by 25.

On to step 1:
If we divide 6 by 25, we get 0 and a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 25

On to step 2:
When dividing 63 by 25, we get 2 with a remainder of 13.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Deduct 50 from 63 and we're left with 13.
Grab the next digit (6) from the dividend, add it to 13, then carry on: 136 / 25

Going ahead to step 3:
25 can be fit into 136 5 times, resulting in a remainder of 11.
Use 5 as the next digit of our solution. 
Result so far: 25.0
Subtracting 125 from 136 leaves us with 11.
Bring next digit (5) of the dividend behind the 11 and repeat the process: 115 / 25

Going ahead to step 4:
25 can be fit into 115 4 times, resulting in a remainder of 15.
Put 4 as the next digit of the answer. 
Result so far: 254.0
If we take 100 away from 115, we end up with 15.
Include the next digit (0) from the dividend after 15, then repeat: 150 / 25

Step 5:
When dividing 150 by 25, we get 6 with a remainder of 0.
The number 6 becomes the next digit in our result. 
Result so far: 2546.0
Subtract 150 from 150 to get 0.
Append the next digit (3) from the dividend to 0 and continue with: 3 / 25

On to step 6:
The number 25 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 25460.0
If we subtract 0 from 3, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 7:
When dividing 30 by 25, we get 1 with a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 25460.1
Subtracting 25 from 30 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
25 goes into 50 2 times with a remainder of 0.
The next digit of our result is 2. 
Result so far: 25460.12
The remainder is 0 after subtracting 50 from 50.
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:
The number 25 fits into 0 0 times, leaving a remainder of 0.
The next digit of our result is 0. 
Result so far: 25460.12
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.

Let's proceed to step 10:
When dividing 0 by 25, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 25460.12
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.

After the division, we end up with 25460.12 and a remainder of 0.0.