638262 ÷ 6 
We want to figure out the number of times 638262 can be divided by 6.

Advancing to step 1:
If we divide 6 by 6, we get 1 and a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 6 from 6 to get 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 6

Moving on to step 2:
If we divide 3 by 6, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 10.0
Deduct 0 from 3 and we're left with 3.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 6

On to step 3:
When dividing 38 by 6, we get 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 106.0
Deduct 36 from 38 and we're left with 2.
Append the next digit (2) from the dividend to 2 and continue with: 22 / 6

On to step 4:
The number 6 fits into 22 3 times, leaving a remainder of 4.
Use 3 as the next digit of our solution. 
Result so far: 1063.0
Subtracting 18 from 22 leaves us with 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 6

Let's proceed to step 5:
6 goes into 46 7 times with a remainder of 4.
Put 7 as the next digit of the answer. 
Result so far: 10637.0
The remainder is 4 after subtracting 42 from 46.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 6

Advancing to step 6:
When dividing 42 by 6, we get 7 with a remainder of 0.
The number 7 becomes the next digit in our result. 
Result so far: 106377.0
Subtract 42 from 42 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 7:
When dividing 0 by 6, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 106377.0
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
The number 6 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 106377.0
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 106377.0, and the remainder is 0.0.