501959 ÷ 6 
We want to figure out the number of times 501959 can be divided by 6.

Advancing to step 1:
6 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 6

Advancing to step 2:
When dividing 50 by 6, we get 8 with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 8.0
Deduct 48 from 50 and we're left with 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 3:
21 divided by 6 is 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 83.0
If we take 18 away from 21, we end up with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 6

On to step 4:
39 divided by 6 is 6 with a remainder of 3.
Record the quotient 6 as the next digit in the result. 
Result so far: 836.0
If we take 36 away from 39, we end up with 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 6

Let's proceed to step 5:
6 can be fit into 35 5 times, resulting in a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 8365.0
The remainder is 5 after subtracting 30 from 35.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 6

Step 6:
59 divided by 6 is 9 with a remainder of 5.
The next digit of our result is 9. 
Result so far: 83659.0
Subtracting 54 from 59 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 7:
6 can be fit into 50 8 times, resulting in a remainder of 2.
The next digit of our result is 8. 
Result so far: 83659.8
Subtracting 48 from 50 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
If we divide 20 by 6, we get 3 and a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 83659.83
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 9:
The number 6 fits into 20 3 times, leaving a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 83659.833
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 83659.833, and the remainder is 0.0002.