We're dividing 516271 by 15 
We want to figure out the number of times 516271 can be divided by 15.

On to step 1:
The number 15 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.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 15

On to step 2:
15 can be fit into 51 3 times, resulting in a remainder of 6.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 6 after subtracting 45 from 51.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 15

Moving on to step 3:
The number 15 fits into 66 4 times, leaving a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 34.0
If we subtract 60 from 66, we get 6.
Fetch the next digit (2) from the dividend, attach it to 6 and continue: 62 / 15

Let's proceed to step 4:
62 divided by 15 is 4 with a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 344.0
Deduct 60 from 62 and we're left with 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 15

On to step 5:
If we divide 27 by 15, we get 1 and a remainder of 12.
The number 1 becomes the next digit in our result. 
Result so far: 3441.0
If we take 15 away from 27, we end up with 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 15

Moving on to step 6:
If we divide 121 by 15, we get 8 and a remainder of 1.
The next digit of our result is 8. 
Result so far: 34418.0
The remainder is 1 after subtracting 120 from 121.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
10 divided by 15 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 34418.0
The remainder is 10 after subtracting 0 from 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 8:
The number 15 fits into 100 6 times, leaving a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 34418.06
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 9:
The number 15 fits into 100 6 times, leaving a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 34418.066
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 34418.066, and the remainder is 0.001.