We're dividing 638214 by 27 
We're looking to find how many times 27 goes into 638214.

Going ahead to step 1:
27 can be fit into 6 0 times, resulting in a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 27

Let's proceed to step 2:
27 goes into 63 2 times with a remainder of 9.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtracting 54 from 63 leaves us with 9.
Append the next digit (8) from the dividend to 9 and continue with: 98 / 27

On to step 3:
The number 27 fits into 98 3 times, leaving a remainder of 17.
Use 3 as the next digit of our solution. 
Result so far: 23.0
Deduct 81 from 98 and we're left with 17.
Fetch the next digit (2) from the dividend, attach it to 17 and continue: 172 / 27

Let's proceed to step 4:
27 can be fit into 172 6 times, resulting in a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 236.0
If we take 162 away from 172, we end up with 10.
Bring next digit (1) of the dividend behind the 10 and repeat the process: 101 / 27

Advancing to step 5:
If we divide 101 by 27, we get 3 and a remainder of 20.
Put 3 as the next digit of the answer. 
Result so far: 2363.0
If we take 81 away from 101, we end up with 20.
Take the next digit (4) from the dividend and append it to 20, then repeat: 204 / 27

On to step 6:
204 divided by 27 is 7 with a remainder of 15.
Put 7 as the next digit of the answer. 
Result so far: 23637.0
If we take 189 away from 204, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 7:
If we divide 150 by 27, we get 5 and a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 23637.5
Subtract 135 from 150 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 8:
When dividing 150 by 27, we get 5 with a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 23637.55
If we subtract 135 from 150, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

In conclusion, the division gives 23637.55 with a balance of 0.015.