257905 ÷ 15 
We're looking to find how many times 15 goes into 257905.

Step 1:
When dividing 2 by 15, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 15

Advancing to step 2:
When dividing 25 by 15, we get 1 with a remainder of 10.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 10 after subtracting 15 from 25.
Fetch the next digit (7) from the dividend, attach it to 10 and continue: 107 / 15

On to step 3:
15 goes into 107 7 times with a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 17.0
Subtract 105 from 107 to get 2.
Grab the next digit (9) from the dividend, add it to 2, then carry on: 29 / 15

Step 4:
The number 15 fits into 29 1 times, leaving a remainder of 14.
Write down 1 as next digit of the result. 
Result so far: 171.0
If we take 15 away from 29, we end up with 14.
Fetch the next digit (0) from the dividend, attach it to 14 and continue: 140 / 15

Let's proceed to step 5:
The number 15 fits into 140 9 times, leaving a remainder of 5.
Use 9 as the next digit of our solution. 
Result so far: 1719.0
The remainder is 5 after subtracting 135 from 140.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 15

Advancing to step 6:
The number 15 fits into 55 3 times, leaving a remainder of 10.
The number 3 becomes the next digit in our result. 
Result so far: 17193.0
If we take 45 away from 55, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 7:
If we divide 100 by 15, we get 6 and a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 17193.6
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
100 divided by 15 is 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 17193.66
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 17193.66 with a balance of 0.01.