We look at the division of 145415 by 13 
We're looking to find how many times 13 goes into 145415.

Going ahead to step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (4) from the dividend and append it to 1, then repeat: 14 / 13

Advancing to step 2:
The number 13 fits into 14 1 times, leaving a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 13 from 14 to get 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 13

Step 3:
If we divide 15 by 13, we get 1 and a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
Subtracting 13 from 15 leaves us with 2.
Include the next digit (4) from the dividend after 2, then repeat: 24 / 13

On to step 4:
The number 13 fits into 24 1 times, leaving a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 111.0
Subtract 13 from 24 to get 11.
Take the next digit (1) from the dividend and append it to 11, then repeat: 111 / 13

Moving on to step 5:
13 goes into 111 8 times with a remainder of 7.
Record the quotient 8 as the next digit in the result. 
Result so far: 1118.0
Subtract 104 from 111 to get 7.
Fetch the next digit (5) from the dividend, attach it to 7 and continue: 75 / 13

Moving on to step 6:
13 can be fit into 75 5 times, resulting in a remainder of 10.
The next digit of our result is 5. 
Result so far: 11185.0
The remainder is 10 after subtracting 65 from 75.
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 7:
13 goes into 100 7 times with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 11185.7
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.

Let's proceed to step 8:
13 can be fit into 90 6 times, resulting in a remainder of 12.
The next digit of our result is 6. 
Result so far: 11185.76
If we subtract 78 from 90, we 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.

On to step 9:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 11185.769
If we take 117 away from 120, we end up 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.

Advancing to step 10:
30 divided by 13 is 2 with a remainder of 4.
The next digit of our result is 2. 
Result so far: 11185.7692
Subtracting 26 from 30 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 11:
13 goes into 40 3 times with a remainder of 1.
The next digit of our result is 3. 
Result so far: 11185.76923
If we take 39 away from 40, we end up 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.

Moving on to step 12:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 11185.76923
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.

Step 13:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 11185.7692307
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.

Going ahead to step 14:
13 goes into 90 6 times with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 11185.76923076
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.

Our division results in 11185.76923076 with a remaining 1.2e-08.