25375402 ÷ 682 
Our goal is to divide 25375402 by 682.

Moving on to step 1:
682 goes into 2 0 times with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 682

Moving on to step 2:
When dividing 25 by 682, we get 0 with a remainder of 25.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 25 to get 25.
Append the next digit (3) from the dividend to 25 and continue with: 253 / 682

Advancing to step 3:
When dividing 253 by 682, we get 0 with a remainder of 253.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 253 after subtracting 0 from 253.
Append the next digit (7) from the dividend to 253 and continue with: 2537 / 682

Moving on to step 4:
The number 682 fits into 2537 3 times, leaving a remainder of 491.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we take 2046 away from 2537, we end up with 491.
Take the next digit (5) from the dividend and append it to 491, then repeat: 4915 / 682

Going ahead to step 5:
When dividing 4915 by 682, we get 7 with a remainder of 141.
The number 7 becomes the next digit in our result. 
Result so far: 37.0
Deduct 4774 from 4915 and we're left with 141.
Grab the next digit (4) from the dividend, add it to 141, then carry on: 1414 / 682

Moving on to step 6:
682 goes into 1414 2 times with a remainder of 50.
Record the quotient 2 as the next digit in the result. 
Result so far: 372.0
Subtract 1364 from 1414 to get 50.
Grab the next digit (0) from the dividend, add it to 50, then carry on: 500 / 682

On to step 7:
When dividing 500 by 682, we get 0 with a remainder of 500.
Put 0 as the next digit of the answer. 
Result so far: 3720.0
Subtract 0 from 500 to get 500.
Fetch the next digit (2) from the dividend, attach it to 500 and continue: 5002 / 682

Moving on to step 8:
682 can be fit into 5002 7 times, resulting in a remainder of 228.
The number 7 becomes the next digit in our result. 
Result so far: 37207.0
Subtracting 4774 from 5002 leaves us with 228.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2280, and continue the process.

Advancing to step 9:
2280 divided by 682 is 3 with a remainder of 234.
Write down 3 as next digit of the result. 
Result so far: 37207.3
Deduct 2046 from 2280 and we're left with 234.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2340, and continue the process.

Let's proceed to step 10:
682 goes into 2340 3 times with a remainder of 294.
The next digit of our result is 3. 
Result so far: 37207.33
Deduct 2046 from 2340 and we're left with 294.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2940, and continue the process.

In conclusion, the division gives 37207.33 with a balance of 0.294.