Let's divide 646441 by 6
Our goal is to divide 646441 by 6.

Moving on to step 1:
6 goes into 6 1 times with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 6 away from 6, we end up with 0.
Fetch the next digit (4) from the dividend, attach it to 0 and continue: 4 / 6

Moving on to step 2:
If we divide 4 by 6, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 10.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 6

Step 3:
46 divided by 6 is 7 with a remainder of 4.
Use 7 as the next digit of our solution. 
Result so far: 107.0
Subtracting 42 from 46 leaves us with 4.
Take the next digit (4) from the dividend and append it to 4, then repeat: 44 / 6

Going ahead to step 4:
The number 6 fits into 44 7 times, leaving a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 1077.0
The remainder is 2 after subtracting 42 from 44.
Grab the next digit (4) from the dividend, add it to 2, then carry on: 24 / 6

Let's proceed to step 5:
When dividing 24 by 6, we get 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 10774.0
If we subtract 24 from 24, we get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Moving on to step 6:
1 divided by 6 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 107740.0
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.

Let's proceed to step 7:
The number 6 fits into 10 1 times, leaving a remainder of 4.
The next digit of our result is 1. 
Result so far: 107740.1
Deduct 6 from 10 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.

Step 8:
When dividing 40 by 6, we get 6 with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 107740.16
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.

Going ahead to step 9:
40 divided by 6 is 6 with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 107740.166
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.

In conclusion, the division gives 107740.166 with a balance of 0.0004.