371306 ÷ 33 
Our goal is to divide 371306 by 33.

On to step 1:
When dividing 3 by 33, we get 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 33

On to step 2:
33 can be fit into 37 1 times, resulting in a remainder of 4.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 4 after subtracting 33 from 37.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 33

Going ahead to step 3:
33 goes into 41 1 times with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
Subtract 33 from 41 to get 8.
Append the next digit (3) from the dividend to 8 and continue with: 83 / 33

Advancing to step 4:
The number 33 fits into 83 2 times, leaving a remainder of 17.
The number 2 becomes the next digit in our result. 
Result so far: 112.0
Subtracting 66 from 83 leaves us with 17.
Append the next digit (0) from the dividend to 17 and continue with: 170 / 33

Moving on to step 5:
When dividing 170 by 33, we get 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 1125.0
If we subtract 165 from 170, we get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 33

Advancing to step 6:
The number 33 fits into 56 1 times, leaving a remainder of 23.
The number 1 becomes the next digit in our result. 
Result so far: 11251.0
If we take 33 away from 56, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 7:
If we divide 230 by 33, we get 6 and a remainder of 32.
Use 6 as the next digit of our solution. 
Result so far: 11251.6
Deduct 198 from 230 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 8:
33 can be fit into 320 9 times, resulting in a remainder of 23.
Put 9 as the next digit of the answer. 
Result so far: 11251.69
Deduct 297 from 320 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 9:
230 divided by 33 is 6 with a remainder of 32.
The number 6 becomes the next digit in our result. 
Result so far: 11251.696
Deduct 198 from 230 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Advancing to step 10:
If we divide 320 by 33, we get 9 and a remainder of 23.
Use 9 as the next digit of our solution. 
Result so far: 11251.6969
Subtracting 297 from 320 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 11:
The number 33 fits into 230 6 times, leaving a remainder of 32.
Use 6 as the next digit of our solution. 
Result so far: 11251.69696
If we take 198 away from 230, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 12:
The number 33 fits into 320 9 times, leaving a remainder of 23.
The next digit of our result is 9. 
Result so far: 11251.696969
If we take 297 away from 320, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 13:
230 divided by 33 is 6 with a remainder of 32.
The number 6 becomes the next digit in our result. 
Result so far: 11251.6969696
Subtracting 198 from 230 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 14:
If we divide 320 by 33, we get 9 and a remainder of 23.
The next digit of our result is 9. 
Result so far: 11251.69696969
Subtract 297 from 320 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

In conclusion, the division gives 11251.69696969 with a balance of 2.3e-08.