We're dividing 637278 by 18 
Our goal is to divide 637278 by 18.

Going ahead to step 1:
When dividing 6 by 18, we get 0 with 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.
Append the next digit (3) from the dividend to 6 and continue with: 63 / 18

On to step 2:
18 goes into 63 3 times with a remainder of 9.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we take 54 away from 63, we end up with 9.
Append the next digit (7) from the dividend to 9 and continue with: 97 / 18

Going ahead to step 3:
18 goes into 97 5 times with a remainder of 7.
Use 5 as the next digit of our solution. 
Result so far: 35.0
If we subtract 90 from 97, we get 7.
Grab the next digit (2) from the dividend, add it to 7, then carry on: 72 / 18

Going ahead to step 4:
The number 18 fits into 72 4 times, leaving a remainder of 0.
The next digit of our result is 4. 
Result so far: 354.0
Deduct 72 from 72 and we're left with 0.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 18

Let's proceed to step 5:
18 can be fit into 7 0 times, resulting in a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 3540.0
Subtracting 0 from 7 leaves us with 7.
Include the next digit (8) from the dividend after 7, then repeat: 78 / 18

Moving on to step 6:
18 goes into 78 4 times with a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 35404.0
Subtracting 72 from 78 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 7:
When dividing 60 by 18, we get 3 with a remainder of 6.
Write down 3 as next digit of the result. 
Result so far: 35404.3
Subtract 54 from 60 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 8:
18 can be fit into 60 3 times, resulting in a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 35404.33
If we take 54 away from 60, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 35404.33 and a remainder of 0.006.