Let's divide 646582 by 6
Our goal is to divide 646582 by 6.

On to step 1:
If we divide 6 by 6, we get 1 and 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.
Fetch the next digit (4) from the dividend, attach it to 0 and continue: 4 / 6

Advancing to step 2:
6 can be fit into 4 0 times, resulting in a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
If we subtract 0 from 4, we get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 6

Step 3:
6 can be fit into 46 7 times, resulting in a remainder of 4.
Use 7 as the next digit of our solution. 
Result so far: 107.0
Deduct 42 from 46 and we're left with 4.
Fetch the next digit (5) from the dividend, attach it to 4 and continue: 45 / 6

Moving on to step 4:
If we divide 45 by 6, we get 7 and a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 1077.0
Subtracting 42 from 45 leaves us with 3.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 6

Going ahead to step 5:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 10776.0
If we take 36 away from 38, we end up with 2.
Fetch the next digit (2) from the dividend, attach it to 2 and continue: 22 / 6

Moving on to step 6:
6 can be fit into 22 3 times, resulting in a remainder of 4.
The next digit of our result is 3. 
Result so far: 107763.0
Deduct 18 from 22 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 7:
6 can be fit into 40 6 times, resulting in a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 107763.6
If we subtract 36 from 40, we 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.

Step 8:
6 can be fit into 40 6 times, resulting in a remainder of 4.
The next digit of our result is 6. 
Result so far: 107763.66
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 107763.66 with a remainder of 0.004.