We look at the division of 261317 by 6 
Our goal is to divide 261317 by 6.

Moving on to step 1:
When dividing 2 by 6, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Append the next digit (6) from the dividend to 2 and continue with: 26 / 6

Let's proceed to step 2:
6 goes into 26 4 times with a remainder of 2.
The next digit of our result is 4. 
Result so far: 4.0
If we take 24 away from 26, we end up with 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 6

Step 3:
If we divide 21 by 6, we get 3 and a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 43.0
Deduct 18 from 21 and we're left with 3.
Grab the next digit (3) from the dividend, add it to 3, then carry on: 33 / 6

Moving on to step 4:
33 divided by 6 is 5 with a remainder of 3.
Record the quotient 5 as the next digit in the result. 
Result so far: 435.0
If we subtract 30 from 33, we get 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 6

Moving on to step 5:
31 divided by 6 is 5 with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 4355.0
The remainder is 1 after subtracting 30 from 31.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 6

Advancing to step 6:
If we divide 17 by 6, we get 2 and a remainder of 5.
Use 2 as the next digit of our solution. 
Result so far: 43552.0
If we subtract 12 from 17, 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.

Advancing to step 7:
The number 6 fits into 50 8 times, leaving a remainder of 2.
The next digit of our result is 8. 
Result so far: 43552.8
If we take 48 away from 50, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
When dividing 20 by 6, we get 3 with a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 43552.83
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 9:
The number 6 fits into 20 3 times, leaving a remainder of 2.
The next digit of our result is 3. 
Result so far: 43552.833
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 43552.833, and the remainder is 0.0002.