25745 ÷ 19 
Our goal is to divide 25745 by 19.

Step 1:
The number 19 fits into 2 0 times, leaving a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 19

On to step 2:
19 goes into 25 1 times with a remainder of 6.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 19 from 25, we get 6.
Fetch the next digit (7) from the dividend, attach it to 6 and continue: 67 / 19

Going ahead to step 3:
19 can be fit into 67 3 times, resulting in a remainder of 10.
Write down 3 as next digit of the result. 
Result so far: 13.0
The remainder is 10 after subtracting 57 from 67.
Grab the next digit (4) from the dividend, add it to 10, then carry on: 104 / 19

On to step 4:
When dividing 104 by 19, we get 5 with a remainder of 9.
The next digit of our result is 5. 
Result so far: 135.0
If we take 95 away from 104, we end up with 9.
Include the next digit (5) from the dividend after 9, then repeat: 95 / 19

Let's proceed to step 5:
95 divided by 19 is 5 with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 1355.0
Deduct 95 from 95 and we're left 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.

Moving on to step 6:
If we divide 0 by 19, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 1355.0
Subtract 0 from 0 to 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.

Step 7:
When dividing 0 by 19, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 1355.0
Deduct 0 from 0 and we're left 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.

The quotient of the division is 1355.0, and the remainder is 0.0.