321135 ÷ 6 
We're looking to find how many times 6 goes into 321135.

Going ahead to step 1:
When dividing 3 by 6, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Append the next digit (2) from the dividend to 3 and continue with: 32 / 6

Going ahead to step 2:
6 goes into 32 5 times with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 5.0
If we take 30 away from 32, we end up with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 6

On to step 3:
21 divided by 6 is 3 with a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 53.0
The remainder is 3 after subtracting 18 from 21.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 6

On to step 4:
When dividing 31 by 6, we get 5 with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 535.0
Subtracting 30 from 31 leaves us with 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 6

Going ahead to step 5:
6 can be fit into 13 2 times, resulting in a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 5352.0
Deduct 12 from 13 and we're left with 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 6

On to step 6:
The number 6 fits into 15 2 times, leaving a remainder of 3.
The next digit of our result is 2. 
Result so far: 53522.0
Subtract 12 from 15 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 7:
6 goes into 30 5 times with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 53522.5
Subtract 30 from 30 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 8:
When dividing 0 by 6, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 53522.5
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.

Going ahead to step 9:
0 divided by 6 is 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 53522.5
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.

The quotient of the division is 53522.5, and the remainder is 0.0.