We're dividing 371557 by 37 
We want to divide 371557 by 37.

Advancing to step 1:
When dividing 3 by 37, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 37

Moving on to step 2:
The number 37 fits into 37 1 times, leaving a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 37 from 37 and we're left with 0.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 37

Moving on to step 3:
1 divided by 37 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 10.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 37

Going ahead to step 4:
15 divided by 37 is 0 with a remainder of 15.
Put 0 as the next digit of the answer. 
Result so far: 100.0
The remainder is 15 after subtracting 0 from 15.
Include the next digit (5) from the dividend after 15, then repeat: 155 / 37

Moving on to step 5:
The number 37 fits into 155 4 times, leaving a remainder of 7.
The next digit of our result is 4. 
Result so far: 1004.0
Deduct 148 from 155 and we're left with 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 37

On to step 6:
37 can be fit into 77 2 times, resulting in a remainder of 3.
Record the quotient 2 as the next digit in the result. 
Result so far: 10042.0
Deduct 74 from 77 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 7:
If we divide 30 by 37, we get 0 and a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 10042.0
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 8:
37 can be fit into 300 8 times, resulting in a remainder of 4.
The next digit of our result is 8. 
Result so far: 10042.08
If we subtract 296 from 300, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 9:
When dividing 40 by 37, we get 1 with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 10042.081
If we take 37 away from 40, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 10:
37 goes into 30 0 times with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 10042.081
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 11:
300 divided by 37 is 8 with a remainder of 4.
The next digit of our result is 8. 
Result so far: 10042.08108
Deduct 296 from 300 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 12:
37 goes into 40 1 times with a remainder of 3.
The next digit of our result is 1. 
Result so far: 10042.081081
If we take 37 away from 40, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 13:
If we divide 30 by 37, we get 0 and a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 10042.081081
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 14:
If we divide 300 by 37, we get 8 and a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 10042.08108108
If we subtract 296 from 300, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

In conclusion, the division gives 10042.08108108 with a balance of 4e-09.