513605 ÷ 39 
We want to divide 513605 by 39.

Advancing to step 1:
39 can be fit into 5 0 times, resulting in a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 39

Let's proceed to step 2:
When dividing 51 by 39, we get 1 with a remainder of 12.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 39 from 51, we get 12.
Bring next digit (3) of the dividend behind the 12 and repeat the process: 123 / 39

Moving on to step 3:
If we divide 123 by 39, we get 3 and a remainder of 6.
Write down 3 as next digit of the result. 
Result so far: 13.0
Subtract 117 from 123 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 39

Advancing to step 4:
If we divide 66 by 39, we get 1 and a remainder of 27.
Record the quotient 1 as the next digit in the result. 
Result so far: 131.0
If we subtract 39 from 66, we get 27.
Take the next digit (0) from the dividend and append it to 27, then repeat: 270 / 39

On to step 5:
270 divided by 39 is 6 with a remainder of 36.
The number 6 becomes the next digit in our result. 
Result so far: 1316.0
Subtracting 234 from 270 leaves us with 36.
Append the next digit (5) from the dividend to 36 and continue with: 365 / 39

Moving on to step 6:
39 goes into 365 9 times with a remainder of 14.
Write down 9 as next digit of the result. 
Result so far: 13169.0
Deduct 351 from 365 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
When dividing 140 by 39, we get 3 with a remainder of 23.
The number 3 becomes the next digit in our result. 
Result so far: 13169.3
If we subtract 117 from 140, we 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.

Advancing to step 8:
230 divided by 39 is 5 with a remainder of 35.
The number 5 becomes the next digit in our result. 
Result so far: 13169.35
Subtracting 195 from 230 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.

Going ahead to step 9:
The number 39 fits into 350 8 times, leaving a remainder of 38.
The next digit of our result is 8. 
Result so far: 13169.358
If we subtract 312 from 350, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 10:
39 goes into 380 9 times with a remainder of 29.
Put 9 as the next digit of the answer. 
Result so far: 13169.3589
If we subtract 351 from 380, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Advancing to step 11:
39 goes into 290 7 times with a remainder of 17.
Use 7 as the next digit of our solution. 
Result so far: 13169.35897
Subtracting 273 from 290 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.

Let's proceed to step 12:
If we divide 170 by 39, we get 4 and a remainder of 14.
Use 4 as the next digit of our solution. 
Result so far: 13169.358974
Subtract 156 from 170 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 13:
39 can be fit into 140 3 times, resulting in a remainder of 23.
The next digit of our result is 3. 
Result so far: 13169.3589743
Subtract 117 from 140 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.

On to step 14:
230 divided by 39 is 5 with a remainder of 35.
The number 5 becomes the next digit in our result. 
Result so far: 13169.35897435
Subtracting 195 from 230 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.

In conclusion, the division gives 13169.35897435 with a balance of 3.5e-08.