We're dividing 256697 by 41 
We're looking to find how many times 41 goes into 256697.

Going ahead to step 1:
41 goes into 2 0 times with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 41

Let's proceed to step 2:
When dividing 25 by 41, we get 0 with a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 25, we get 25.
Fetch the next digit (6) from the dividend, attach it to 25 and continue: 256 / 41

Let's proceed to step 3:
When dividing 256 by 41, we get 6 with a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Subtract 246 from 256 to get 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 41

Going ahead to step 4:
41 can be fit into 106 2 times, resulting in a remainder of 24.
Put 2 as the next digit of the answer. 
Result so far: 62.0
The remainder is 24 after subtracting 82 from 106.
Fetch the next digit (9) from the dividend, attach it to 24 and continue: 249 / 41

Step 5:
41 goes into 249 6 times with a remainder of 3.
The next digit of our result is 6. 
Result so far: 626.0
The remainder is 3 after subtracting 246 from 249.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 41

Step 6:
If we divide 37 by 41, we get 0 and a remainder of 37.
The next digit of our result is 0. 
Result so far: 6260.0
If we take 0 away from 37, we end up with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

On to step 7:
The number 41 fits into 370 9 times, leaving a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 6260.9
If we take 369 away from 370, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 8:
When dividing 10 by 41, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 6260.9
If we subtract 0 from 10, we 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.

Step 9:
The number 41 fits into 100 2 times, leaving a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 6260.902
The remainder is 18 after subtracting 82 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 10:
If we divide 180 by 41, we get 4 and a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 6260.9024
The remainder is 16 after subtracting 164 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 11:
41 can be fit into 160 3 times, resulting in a remainder of 37.
Use 3 as the next digit of our solution. 
Result so far: 6260.90243
Subtract 123 from 160 to get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Let's proceed to step 12:
370 divided by 41 is 9 with a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 6260.902439
Subtracting 369 from 370 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 13:
If we divide 10 by 41, we get 0 and a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 6260.902439
Deduct 0 from 10 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.

Moving on to step 14:
41 goes into 100 2 times with a remainder of 18.
The next digit of our result is 2. 
Result so far: 6260.90243902
Subtract 82 from 100 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

After the division, we end up with 6260.90243902 and a remainder of 1.8e-08.