6337 divided by 30 
We want to divide 6337 by 30.

Step 1:
6 divided by 30 is 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 30

Moving on to step 2:
When dividing 63 by 30, we get 2 with a remainder of 3.
The next digit of our result is 2. 
Result so far: 2.0
If we take 60 away from 63, we end up with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 30

Let's proceed to step 3:
When dividing 33 by 30, we get 1 with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 21.0
If we take 30 away from 33, we end up with 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 30

Advancing to step 4:
The number 30 fits into 37 1 times, leaving a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 211.0
If we subtract 30 from 37, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 5:
30 can be fit into 70 2 times, resulting in a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 211.2
Subtracting 60 from 70 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 6:
If we divide 100 by 30, we get 3 and a remainder of 10.
Write down 3 as next digit of the result. 
Result so far: 211.23
Subtracting 90 from 100 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 7:
100 divided by 30 is 3 with a remainder of 10.
The number 3 becomes the next digit in our result. 
Result so far: 211.233
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 211.233 with a balance of 0.001.