514437 divided by 13 
We're looking to find how many times 13 goes into 514437.

Step 1:
When dividing 5 by 13, we get 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 13

Moving on to step 2:
When dividing 51 by 13, we get 3 with a remainder of 12.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we subtract 39 from 51, we get 12.
Fetch the next digit (4) from the dividend, attach it to 12 and continue: 124 / 13

Step 3:
13 goes into 124 9 times with a remainder of 7.
Record the quotient 9 as the next digit in the result. 
Result so far: 39.0
Deduct 117 from 124 and we're left with 7.
Fetch the next digit (4) from the dividend, attach it to 7 and continue: 74 / 13

Going ahead to step 4:
13 goes into 74 5 times with a remainder of 9.
Record the quotient 5 as the next digit in the result. 
Result so far: 395.0
If we take 65 away from 74, we end up with 9.
Fetch the next digit (3) from the dividend, attach it to 9 and continue: 93 / 13

Going ahead to step 5:
The number 13 fits into 93 7 times, leaving a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 3957.0
The remainder is 2 after subtracting 91 from 93.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 13

Moving on to step 6:
The number 13 fits into 27 2 times, leaving a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 39572.0
The remainder is 1 after subtracting 26 from 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
10 divided by 13 is 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 39572.0
If we take 0 away from 10, we end up 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.

On to step 8:
100 divided by 13 is 7 with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 39572.07
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 9:
13 goes into 90 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 39572.076
Subtract 78 from 90 to get 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 10:
120 divided by 13 is 9 with a remainder of 3.
The next digit of our result is 9. 
Result so far: 39572.0769
Subtracting 117 from 120 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 11:
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: 39572.07692
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 12:
If we divide 40 by 13, we get 3 and a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 39572.076923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 13:
When dividing 10 by 13, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 39572.076923
Deduct 0 from 10 and we're left 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.

Advancing to step 14:
13 can be fit into 100 7 times, resulting in a remainder of 9.
The next digit of our result is 7. 
Result so far: 39572.07692307
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Our division results in 39572.07692307 with a remaining 9e-09.