We're dividing 501557 by 37 
Let's see how many times 37 fits into 501557.

Advancing to step 1:
The number 37 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 37

Advancing to step 2:
37 goes into 50 1 times with a remainder of 13.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 37 from 50 and we're left with 13.
Take the next digit (1) from the dividend and append it to 13, then repeat: 131 / 37

Advancing to step 3:
If we divide 131 by 37, we get 3 and a remainder of 20.
Put 3 as the next digit of the answer. 
Result so far: 13.0
Subtract 111 from 131 to get 20.
Grab the next digit (5) from the dividend, add it to 20, then carry on: 205 / 37

Step 4:
37 can be fit into 205 5 times, resulting in a remainder of 20.
The next digit of our result is 5. 
Result so far: 135.0
If we subtract 185 from 205, we get 20.
Grab the next digit (5) from the dividend, add it to 20, then carry on: 205 / 37

Going ahead to step 5:
205 divided by 37 is 5 with a remainder of 20.
Record the quotient 5 as the next digit in the result. 
Result so far: 1355.0
Deduct 185 from 205 and we're left with 20.
Take the next digit (7) from the dividend and append it to 20, then repeat: 207 / 37

Advancing to step 6:
The number 37 fits into 207 5 times, leaving a remainder of 22.
Use 5 as the next digit of our solution. 
Result so far: 13555.0
Deduct 185 from 207 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 7:
If we divide 220 by 37, we get 5 and a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 13555.5
If we subtract 185 from 220, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 8:
37 goes into 350 9 times with a remainder of 17.
The number 9 becomes the next digit in our result. 
Result so far: 13555.59
Subtract 333 from 350 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Step 9:
The number 37 fits into 170 4 times, leaving a remainder of 22.
Use 4 as the next digit of our solution. 
Result so far: 13555.594
If we subtract 148 from 170, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 10:
When dividing 220 by 37, we get 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 13555.5945
If we subtract 185 from 220, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 11:
350 divided by 37 is 9 with a remainder of 17.
Record the quotient 9 as the next digit in the result. 
Result so far: 13555.59459
If we take 333 away from 350, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

On to step 12:
37 goes into 170 4 times with a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 13555.594594
If we subtract 148 from 170, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 13:
37 can be fit into 220 5 times, resulting in a remainder of 35.
Write down 5 as next digit of the result. 
Result so far: 13555.5945945
Subtracting 185 from 220 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 14:
The number 37 fits into 350 9 times, leaving a remainder of 17.
Record the quotient 9 as the next digit in the result. 
Result so far: 13555.59459459
Subtracting 333 from 350 leaves us with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

In conclusion, the division gives 13555.59459459 with a balance of 1.7e-08.