25774141 ÷ 258 
We're looking to find how many times 258 goes into 25774141.

Going ahead to step 1:
2 divided by 258 is 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 258

Going ahead to step 2:
When dividing 25 by 258, we get 0 with a remainder of 25.
Record the quotient 0 as the next digit in the result. 
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 / 258

Moving on to step 3:
258 can be fit into 257 0 times, resulting in a remainder of 257.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 257 to get 257.
Fetch the next digit (7) from the dividend, attach it to 257 and continue: 2577 / 258

Let's proceed to step 4:
258 goes into 2577 9 times with a remainder of 255.
The next digit of our result is 9. 
Result so far: 9.0
Subtract 2322 from 2577 to get 255.
Grab the next digit (4) from the dividend, add it to 255, then carry on: 2554 / 258

Advancing to step 5:
258 goes into 2554 9 times with a remainder of 232.
Use 9 as the next digit of our solution. 
Result so far: 99.0
Subtracting 2322 from 2554 leaves us with 232.
Take the next digit (1) from the dividend and append it to 232, then repeat: 2321 / 258

Step 6:
258 can be fit into 2321 8 times, resulting in a remainder of 257.
Put 8 as the next digit of the answer. 
Result so far: 998.0
The remainder is 257 after subtracting 2064 from 2321.
Include the next digit (4) from the dividend after 257, then repeat: 2574 / 258

Let's proceed to step 7:
When dividing 2574 by 258, we get 9 with a remainder of 252.
The next digit of our result is 9. 
Result so far: 9989.0
Deduct 2322 from 2574 and we're left with 252.
Bring next digit (1) of the dividend behind the 252 and repeat the process: 2521 / 258

On to step 8:
The number 258 fits into 2521 9 times, leaving a remainder of 199.
The next digit of our result is 9. 
Result so far: 99899.0
If we subtract 2322 from 2521, we get 199.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1990, and continue the process.

Let's proceed to step 9:
The number 258 fits into 1990 7 times, leaving a remainder of 184.
Record the quotient 7 as the next digit in the result. 
Result so far: 99899.7
Deduct 1806 from 1990 and we're left with 184.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1840, and continue the process.

Step 10:
When dividing 1840 by 258, we get 7 with a remainder of 34.
Write down 7 as next digit of the result. 
Result so far: 99899.77
If we subtract 1806 from 1840, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

The final result is 99899.77 with a remainder of 0.034.