We look at the division of 513588 by 3 
We want to divide 513588 by 3.

On to step 1:
When dividing 5 by 3, we get 1 with a remainder of 2.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 3 from 5, we get 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 3

On to step 2:
3 can be fit into 21 7 times, resulting in a remainder of 0.
The number 7 becomes the next digit in our result. 
Result so far: 17.0
If we take 21 away from 21, we end up with 0.
Fetch the next digit (3) from the dividend, attach it to 0 and continue: 3 / 3

Advancing to step 3:
3 goes into 3 1 times with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 171.0
Deduct 3 from 3 and we're left with 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 3

Moving on to step 4:
The number 3 fits into 5 1 times, leaving a remainder of 2.
The next digit of our result is 1. 
Result so far: 1711.0
Subtracting 3 from 5 leaves us with 2.
Include the next digit (8) from the dividend after 2, then repeat: 28 / 3

Step 5:
3 can be fit into 28 9 times, resulting in a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 17119.0
If we take 27 away from 28, we end up with 1.
Include the next digit (8) from the dividend after 1, then repeat: 18 / 3

Step 6:
The number 3 fits into 18 6 times, leaving a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 171196.0
If we subtract 18 from 18, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 7:
The number 3 fits into 0 0 times, leaving a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 171196.0
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
The number 3 fits into 0 0 times, leaving a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 171196.0
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 171196.0, and the remainder is 0.0.