We look at the division of 306357 by 37 
Our goal is to divide 306357 by 37.

Step 1:
3 divided by 37 is 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Grab the next digit (0) from the dividend, add it to 3, then carry on: 30 / 37

Step 2:
37 can be fit into 30 0 times, resulting in a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 30 after subtracting 0 from 30.
Take the next digit (6) from the dividend and append it to 30, then repeat: 306 / 37

Advancing to step 3:
37 goes into 306 8 times with a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we subtract 296 from 306, we get 10.
Take the next digit (3) from the dividend and append it to 10, then repeat: 103 / 37

Advancing to step 4:
37 goes into 103 2 times with a remainder of 29.
The number 2 becomes the next digit in our result. 
Result so far: 82.0
If we take 74 away from 103, we end up with 29.
Include the next digit (5) from the dividend after 29, then repeat: 295 / 37

Advancing to step 5:
When dividing 295 by 37, we get 7 with a remainder of 36.
The number 7 becomes the next digit in our result. 
Result so far: 827.0
If we take 259 away from 295, we end up with 36.
Bring next digit (7) of the dividend behind the 36 and repeat the process: 367 / 37

Advancing to step 6:
The number 37 fits into 367 9 times, leaving a remainder of 34.
The next digit of our result is 9. 
Result so far: 8279.0
Deduct 333 from 367 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 7:
37 goes into 340 9 times with a remainder of 7.
The next digit of our result is 9. 
Result so far: 8279.9
If we subtract 333 from 340, 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.

Moving on to step 8:
70 divided by 37 is 1 with a remainder of 33.
Record the quotient 1 as the next digit in the result. 
Result so far: 8279.91
Deduct 37 from 70 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 9:
37 goes into 330 8 times with a remainder of 34.
The next digit of our result is 8. 
Result so far: 8279.918
Subtract 296 from 330 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 10:
340 divided by 37 is 9 with a remainder of 7.
Use 9 as the next digit of our solution. 
Result so far: 8279.9189
Deduct 333 from 340 and we're left with 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 11:
37 can be fit into 70 1 times, resulting in a remainder of 33.
The number 1 becomes the next digit in our result. 
Result so far: 8279.91891
Deduct 37 from 70 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 12:
330 divided by 37 is 8 with a remainder of 34.
The number 8 becomes the next digit in our result. 
Result so far: 8279.918918
If we subtract 296 from 330, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 13:
When dividing 340 by 37, we get 9 with a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 8279.9189189
The remainder is 7 after subtracting 333 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 14:
If we divide 70 by 37, we get 1 and a remainder of 33.
Put 1 as the next digit of the answer. 
Result so far: 8279.91891891
If we take 37 away from 70, we end up with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

The final result is 8279.91891891 with a remainder of 3.3e-08.