We look at the division of 25792514 by 688 
Our goal is to divide 25792514 by 688.

Advancing to step 1:
If we divide 2 by 688, we get 0 and 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.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 688

Advancing to step 2:
When dividing 25 by 688, we get 0 with a remainder of 25.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 25 to get 25.
Fetch the next digit (7) from the dividend, attach it to 25 and continue: 257 / 688

Let's proceed to step 3:
If we divide 257 by 688, we get 0 and a remainder of 257.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 257, we get 257.
Include the next digit (9) from the dividend after 257, then repeat: 2579 / 688

Advancing to step 4:
2579 divided by 688 is 3 with a remainder of 515.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Subtracting 2064 from 2579 leaves us with 515.
Fetch the next digit (2) from the dividend, attach it to 515 and continue: 5152 / 688

On to step 5:
When dividing 5152 by 688, we get 7 with a remainder of 336.
Use 7 as the next digit of our solution. 
Result so far: 37.0
Deduct 4816 from 5152 and we're left with 336.
Include the next digit (5) from the dividend after 336, then repeat: 3365 / 688

Step 6:
If we divide 3365 by 688, we get 4 and a remainder of 613.
Record the quotient 4 as the next digit in the result. 
Result so far: 374.0
If we take 2752 away from 3365, we end up with 613.
Grab the next digit (1) from the dividend, add it to 613, then carry on: 6131 / 688

On to step 7:
688 can be fit into 6131 8 times, resulting in a remainder of 627.
The next digit of our result is 8. 
Result so far: 3748.0
If we take 5504 away from 6131, we end up with 627.
Fetch the next digit (4) from the dividend, attach it to 627 and continue: 6274 / 688

Step 8:
The number 688 fits into 6274 9 times, leaving a remainder of 82.
Put 9 as the next digit of the answer. 
Result so far: 37489.0
If we take 6192 away from 6274, we end up with 82.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

Moving on to step 9:
If we divide 820 by 688, we get 1 and a remainder of 132.
The number 1 becomes the next digit in our result. 
Result so far: 37489.1
Subtracting 688 from 820 leaves us with 132.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1320, and continue the process.

Let's proceed to step 10:
The number 688 fits into 1320 1 times, leaving a remainder of 632.
Put 1 as the next digit of the answer. 
Result so far: 37489.11
If we subtract 688 from 1320, we get 632.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6320, and continue the process.

In conclusion, the division gives 37489.11 with a balance of 0.632.