We look at the division of 369837 by 34 
Our goal is to divide 369837 by 34.

Advancing to step 1:
The number 34 fits into 3 0 times, leaving a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 34

Moving on to step 2:
34 can be fit into 36 1 times, resulting in a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 34 away from 36, we end up with 2.
Append the next digit (9) from the dividend to 2 and continue with: 29 / 34

Let's proceed to step 3:
If we divide 29 by 34, we get 0 and a remainder of 29.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we subtract 0 from 29, we get 29.
Append the next digit (8) from the dividend to 29 and continue with: 298 / 34

Going ahead to step 4:
If we divide 298 by 34, we get 8 and a remainder of 26.
Record the quotient 8 as the next digit in the result. 
Result so far: 108.0
If we take 272 away from 298, we end up with 26.
Fetch the next digit (3) from the dividend, attach it to 26 and continue: 263 / 34

Moving on to step 5:
34 can be fit into 263 7 times, resulting in a remainder of 25.
Record the quotient 7 as the next digit in the result. 
Result so far: 1087.0
If we take 238 away from 263, we end up with 25.
Take the next digit (7) from the dividend and append it to 25, then repeat: 257 / 34

Advancing to step 6:
34 can be fit into 257 7 times, resulting in a remainder of 19.
Record the quotient 7 as the next digit in the result. 
Result so far: 10877.0
Deduct 238 from 257 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 7:
34 can be fit into 190 5 times, resulting in a remainder of 20.
Record the quotient 5 as the next digit in the result. 
Result so far: 10877.5
The remainder is 20 after subtracting 170 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
34 can be fit into 200 5 times, resulting in a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 10877.55
If we take 170 away from 200, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 10877.55 with a balance of 0.03.