513997 ÷ 35 
Our goal is to divide 513997 by 35.

Advancing to step 1:
35 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 35

Advancing to step 2:
When dividing 51 by 35, we get 1 with a remainder of 16.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 35 from 51 leaves us with 16.
Fetch the next digit (3) from the dividend, attach it to 16 and continue: 163 / 35

Step 3:
35 goes into 163 4 times with a remainder of 23.
Use 4 as the next digit of our solution. 
Result so far: 14.0
The remainder is 23 after subtracting 140 from 163.
Include the next digit (9) from the dividend after 23, then repeat: 239 / 35

Let's proceed to step 4:
When dividing 239 by 35, we get 6 with a remainder of 29.
Record the quotient 6 as the next digit in the result. 
Result so far: 146.0
If we take 210 away from 239, we end up with 29.
Take the next digit (9) from the dividend and append it to 29, then repeat: 299 / 35

Advancing to step 5:
35 goes into 299 8 times with a remainder of 19.
Record the quotient 8 as the next digit in the result. 
Result so far: 1468.0
If we subtract 280 from 299, we get 19.
Bring next digit (7) of the dividend behind the 19 and repeat the process: 197 / 35

On to step 6:
35 can be fit into 197 5 times, resulting in a remainder of 22.
The next digit of our result is 5. 
Result so far: 14685.0
The remainder is 22 after subtracting 175 from 197.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 7:
The number 35 fits into 220 6 times, leaving a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 14685.6
Subtract 210 from 220 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
100 divided by 35 is 2 with a remainder of 30.
The number 2 becomes the next digit in our result. 
Result so far: 14685.62
Deduct 70 from 100 and we're left with 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 9:
When dividing 300 by 35, we get 8 with a remainder of 20.
Use 8 as the next digit of our solution. 
Result so far: 14685.628
If we subtract 280 from 300, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 10:
When dividing 200 by 35, we get 5 with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 14685.6285
If we take 175 away from 200, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 11:
The number 35 fits into 250 7 times, leaving a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 14685.62857
Subtract 245 from 250 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 12:
35 goes into 50 1 times with a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 14685.628571
Deduct 35 from 50 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 13:
35 goes into 150 4 times with a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 14685.6285714
Subtracting 140 from 150 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 14:
If we divide 100 by 35, we get 2 and a remainder of 30.
Write down 2 as next digit of the result. 
Result so far: 14685.62857142
If we take 70 away from 100, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The quotient of the division is 14685.62857142, and the remainder is 3e-08.