We're dividing 353461 by 6 
We're looking to find how many times 6 goes into 353461.

Advancing to step 1:
When dividing 3 by 6, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 6

Step 2:
If we divide 35 by 6, we get 5 and a remainder of 5.
The next digit of our result is 5. 
Result so far: 5.0
Subtracting 30 from 35 leaves us with 5.
Take the next digit (3) from the dividend and append it to 5, then repeat: 53 / 6

Moving on to step 3:
If we divide 53 by 6, we get 8 and a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 58.0
Subtracting 48 from 53 leaves us with 5.
Include the next digit (4) from the dividend after 5, then repeat: 54 / 6

On to step 4:
If we divide 54 by 6, we get 9 and a remainder of 0.
The next digit of our result is 9. 
Result so far: 589.0
Subtract 54 from 54 to get 0.
Take the next digit (6) from the dividend and append it to 0, then repeat: 6 / 6

Let's proceed to step 5:
When dividing 6 by 6, we get 1 with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 5891.0
If we subtract 6 from 6, we get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

On to step 6:
6 can be fit into 1 0 times, resulting in a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 58910.0
If we take 0 away from 1, 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 7:
6 goes into 10 1 times with a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 58910.1
If we take 6 away from 10, 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.

Let's proceed to step 8:
The number 6 fits into 40 6 times, leaving a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 58910.16
The remainder is 4 after subtracting 36 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 9:
40 divided by 6 is 6 with a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 58910.166
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.

Our division results in 58910.166 with a remaining 0.0004.