We look at the division of 637288 by 25 
We want to divide 637288 by 25.

Advancing to step 1:
When dividing 6 by 25, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 25

Moving on to step 2:
When dividing 63 by 25, we get 2 with a remainder of 13.
Write down 2 as next digit of the result. 
Result so far: 2.0
If we take 50 away from 63, we end up with 13.
Take the next digit (7) from the dividend and append it to 13, then repeat: 137 / 25

Going ahead to step 3:
25 goes into 137 5 times with a remainder of 12.
The number 5 becomes the next digit in our result. 
Result so far: 25.0
Subtract 125 from 137 to get 12.
Bring next digit (2) of the dividend behind the 12 and repeat the process: 122 / 25

Going ahead to step 4:
122 divided by 25 is 4 with a remainder of 22.
The next digit of our result is 4. 
Result so far: 254.0
If we subtract 100 from 122, we get 22.
Include the next digit (8) from the dividend after 22, then repeat: 228 / 25

On to step 5:
If we divide 228 by 25, we get 9 and a remainder of 3.
The next digit of our result is 9. 
Result so far: 2549.0
If we subtract 225 from 228, we get 3.
Grab the next digit (8) from the dividend, add it to 3, then carry on: 38 / 25

Step 6:
25 goes into 38 1 times with a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 25491.0
If we take 25 away from 38, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 7:
25 goes into 130 5 times with a remainder of 5.
The next digit of our result is 5. 
Result so far: 25491.5
The remainder is 5 after subtracting 125 from 130.
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.
Record the quotient 2 as the next digit in the result. 
Result so far: 25491.52
Subtracting 50 from 50 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.

Let's proceed 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: 25491.52
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 next digit of our result is 0. 
Result so far: 25491.52
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.

The final result is 25491.52 with a remainder of 0.0.