513957 divided by 37 
We're looking to find how many times 37 goes into 513957.

Let's proceed to step 1:
37 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 37

Going ahead to step 2:
51 divided by 37 is 1 with a remainder of 14.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 37 from 51, we get 14.
Take the next digit (3) from the dividend and append it to 14, then repeat: 143 / 37

Moving on to step 3:
37 can be fit into 143 3 times, resulting in a remainder of 32.
Put 3 as the next digit of the answer. 
Result so far: 13.0
If we subtract 111 from 143, we get 32.
Grab the next digit (9) from the dividend, add it to 32, then carry on: 329 / 37

Step 4:
If we divide 329 by 37, we get 8 and a remainder of 33.
Write down 8 as next digit of the result. 
Result so far: 138.0
If we subtract 296 from 329, we get 33.
Append the next digit (5) from the dividend to 33 and continue with: 335 / 37

Moving on to step 5:
37 goes into 335 9 times with a remainder of 2.
The next digit of our result is 9. 
Result so far: 1389.0
Deduct 333 from 335 and we're left with 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 37

Advancing to step 6:
The number 37 fits into 27 0 times, leaving a remainder of 27.
Use 0 as the next digit of our solution. 
Result so far: 13890.0
If we subtract 0 from 27, we get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 7:
270 divided by 37 is 7 with a remainder of 11.
Use 7 as the next digit of our solution. 
Result so far: 13890.7
If we subtract 259 from 270, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 8:
110 divided by 37 is 2 with a remainder of 36.
Use 2 as the next digit of our solution. 
Result so far: 13890.72
If we take 74 away from 110, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 9:
360 divided by 37 is 9 with a remainder of 27.
Put 9 as the next digit of the answer. 
Result so far: 13890.729
Subtract 333 from 360 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Moving on to step 10:
The number 37 fits into 270 7 times, leaving a remainder of 11.
Record the quotient 7 as the next digit in the result. 
Result so far: 13890.7297
Deduct 259 from 270 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 11:
37 can be fit into 110 2 times, resulting in a remainder of 36.
The number 2 becomes the next digit in our result. 
Result so far: 13890.72972
If we take 74 away from 110, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 12:
If we divide 360 by 37, we get 9 and a remainder of 27.
Record the quotient 9 as the next digit in the result. 
Result so far: 13890.729729
If we take 333 away from 360, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Advancing to step 13:
37 can be fit into 270 7 times, resulting in a remainder of 11.
Record the quotient 7 as the next digit in the result. 
Result so far: 13890.7297297
Deduct 259 from 270 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 14:
The number 37 fits into 110 2 times, leaving a remainder of 36.
The number 2 becomes the next digit in our result. 
Result so far: 13890.72972972
The remainder is 36 after subtracting 74 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

In conclusion, the division gives 13890.72972972 with a balance of 3.6e-08.