We look at the division of 633274 by 6 
Our goal is to divide 633274 by 6.

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
If we subtract 6 from 6, we get 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 6

Let's proceed to step 2:
The number 6 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 10.0
If we subtract 0 from 3, we get 3.
Grab the next digit (3) from the dividend, add it to 3, then carry on: 33 / 6

Advancing to step 3:
The number 6 fits into 33 5 times, leaving a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 105.0
Subtracting 30 from 33 leaves us with 3.
Take the next digit (2) from the dividend and append it to 3, then repeat: 32 / 6

Moving on to step 4:
6 goes into 32 5 times with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 1055.0
Subtract 30 from 32 to get 2.
Grab the next digit (7) from the dividend, add it to 2, then carry on: 27 / 6

Let's proceed to step 5:
The number 6 fits into 27 4 times, leaving a remainder of 3.
The next digit of our result is 4. 
Result so far: 10554.0
Deduct 24 from 27 and we're left with 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 6

Let's proceed to step 6:
When dividing 34 by 6, we get 5 with a remainder of 4.
Record the quotient 5 as the next digit in the result. 
Result so far: 105545.0
The remainder is 4 after subtracting 30 from 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
If we divide 40 by 6, we get 6 and a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 105545.6
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.

Going ahead to step 8:
6 can be fit into 40 6 times, resulting in a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 105545.66
If we take 36 away from 40, we end up 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.

After the division, we end up with 105545.66 and a remainder of 0.004.