514914 ÷ 13 
We're looking to find how many times 13 goes into 514914.

On to step 1:
13 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 13

Advancing to step 2:
If we divide 51 by 13, we get 3 and a remainder of 12.
The next digit of our result is 3. 
Result so far: 3.0
Subtract 39 from 51 to get 12.
Grab the next digit (4) from the dividend, add it to 12, then carry on: 124 / 13

Advancing to step 3:
The number 13 fits into 124 9 times, leaving a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 39.0
Deduct 117 from 124 and we're left with 7.
Include the next digit (9) from the dividend after 7, then repeat: 79 / 13

Moving on to step 4:
If we divide 79 by 13, we get 6 and a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 396.0
If we subtract 78 from 79, we get 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 13

Going ahead to step 5:
11 divided by 13 is 0 with a remainder of 11.
The next digit of our result is 0. 
Result so far: 3960.0
If we subtract 0 from 11, we get 11.
Append the next digit (4) from the dividend to 11 and continue with: 114 / 13

Let's proceed to step 6:
When dividing 114 by 13, we get 8 with a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 39608.0
If we subtract 104 from 114, we 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 7:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 39608.7
If we take 91 away from 100, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 8:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 39608.76
Deduct 78 from 90 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 9:
If we divide 120 by 13, we get 9 and a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 39608.769
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 10:
If we divide 30 by 13, we get 2 and a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 39608.7692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 11:
40 divided by 13 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 39608.76923
Subtracting 39 from 40 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 12:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 39608.76923
Subtracting 0 from 10 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.

Going ahead to step 13:
If we divide 100 by 13, we get 7 and a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 39608.7692307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 14:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The next digit of our result is 6. 
Result so far: 39608.76923076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 39608.76923076 with a balance of 1.2e-08.