617755 ÷ 6 
We're looking to find how many times 6 goes into 617755.

Advancing to step 1:
When dividing 6 by 6, we get 1 with a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 6 away from 6, we end up with 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 6

Moving on to step 2:
When dividing 1 by 6, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 6

Moving on to step 3:
When dividing 17 by 6, we get 2 with a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 102.0
If we subtract 12 from 17, we get 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 6

Going ahead to step 4:
The number 6 fits into 57 9 times, leaving a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 1029.0
Deduct 54 from 57 and we're left with 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Advancing to step 5:
The number 6 fits into 35 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 10295.0
If we subtract 30 from 35, we get 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 6

Advancing to step 6:
If we divide 55 by 6, we get 9 and a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 102959.0
Subtracting 54 from 55 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.

On to step 7:
If we divide 10 by 6, we get 1 and a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 102959.1
The remainder is 4 after subtracting 6 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
6 goes into 40 6 times with a remainder of 4.
The next digit of our result is 6. 
Result so far: 102959.16
Subtract 36 from 40 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 9:
40 divided by 6 is 6 with a remainder of 4.
The next digit of our result is 6. 
Result so far: 102959.166
If we take 36 away from 40, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 102959.166, and the remainder is 0.0004.