We look at the division of 645743 by 25 
We want to divide 645743 by 25.

Step 1:
The number 25 fits into 6 0 times, leaving a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 25

Let's proceed to step 2:
If we divide 64 by 25, we get 2 and a remainder of 14.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Deduct 50 from 64 and we're left with 14.
Fetch the next digit (5) from the dividend, attach it to 14 and continue: 145 / 25

Moving on to step 3:
25 can be fit into 145 5 times, resulting in a remainder of 20.
Put 5 as the next digit of the answer. 
Result so far: 25.0
If we subtract 125 from 145, we get 20.
Grab the next digit (7) from the dividend, add it to 20, then carry on: 207 / 25

Going ahead to step 4:
25 goes into 207 8 times with a remainder of 7.
Write down 8 as next digit of the result. 
Result so far: 258.0
If we subtract 200 from 207, we get 7.
Take the next digit (4) from the dividend and append it to 7, then repeat: 74 / 25

Going ahead to step 5:
25 can be fit into 74 2 times, resulting in a remainder of 24.
Put 2 as the next digit of the answer. 
Result so far: 2582.0
If we take 50 away from 74, we end up with 24.
Take the next digit (3) from the dividend and append it to 24, then repeat: 243 / 25

Moving on to step 6:
243 divided by 25 is 9 with a remainder of 18.
Put 9 as the next digit of the answer. 
Result so far: 25829.0
The remainder is 18 after subtracting 225 from 243.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 7:
When dividing 180 by 25, we get 7 with a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 25829.7
If we subtract 175 from 180, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
50 divided by 25 is 2 with a remainder of 0.
The number 2 becomes the next digit in our result. 
Result so far: 25829.72
Subtract 50 from 50 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.

Let's proceed to step 9:
25 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 25829.72
Subtracting 0 from 0 leaves us 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.

Advancing to step 10:
25 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 25829.72
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 25829.72 and a remainder of 0.0.