Let's divide 641743 by 6
We're looking to find how many times 6 goes into 641743.

On to step 1:
If we divide 6 by 6, we get 1 and a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 6 from 6 leaves us with 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 6

Advancing to step 2:
6 can be fit into 4 0 times, resulting in a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Deduct 0 from 4 and we're left with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 6

Let's proceed to step 3:
If we divide 41 by 6, we get 6 and a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 106.0
Subtracting 36 from 41 leaves us with 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 6

Step 4:
6 can be fit into 57 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 1069.0
Subtract 54 from 57 to get 3.
Grab the next digit (4) from the dividend, add it to 3, then carry on: 34 / 6

On to step 5:
6 goes into 34 5 times with a remainder of 4.
Record the quotient 5 as the next digit in the result. 
Result so far: 10695.0
Subtracting 30 from 34 leaves us with 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 6

Moving on to step 6:
6 goes into 43 7 times with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 106957.0
Subtracting 42 from 43 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.

Let's proceed to step 7:
6 goes into 10 1 times with a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 106957.1
Subtract 6 from 10 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.

On to step 8:
If we divide 40 by 6, we get 6 and a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 106957.16
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:
6 goes into 40 6 times with a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 106957.166
Deduct 36 from 40 and we're left 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 final result is 106957.166 with a remainder of 0.0004.