We're dividing 345614 by 13 
We want to divide 345614 by 13.

Advancing to step 1:
The number 13 fits into 3 0 times, leaving a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 13

Let's proceed to step 2:
34 divided by 13 is 2 with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 2.0
If we subtract 26 from 34, we get 8.
Bring next digit (5) of the dividend behind the 8 and repeat the process: 85 / 13

Moving on to step 3:
If we divide 85 by 13, we get 6 and a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 26.0
The remainder is 7 after subtracting 78 from 85.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 13

Let's proceed to step 4:
If we divide 76 by 13, we get 5 and a remainder of 11.
Put 5 as the next digit of the answer. 
Result so far: 265.0
If we subtract 65 from 76, we get 11.
Fetch the next digit (1) from the dividend, attach it to 11 and continue: 111 / 13

On to step 5:
13 can be fit into 111 8 times, resulting in a remainder of 7.
The number 8 becomes the next digit in our result. 
Result so far: 2658.0
Deduct 104 from 111 and we're left with 7.
Take the next digit (4) from the dividend and append it to 7, then repeat: 74 / 13

On to step 6:
13 can be fit into 74 5 times, resulting in a remainder of 9.
Record the quotient 5 as the next digit in the result. 
Result so far: 26585.0
The remainder is 9 after subtracting 65 from 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 7:
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: 26585.6
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 8:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 26585.69
Deduct 117 from 120 and we're left 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.

Going ahead to step 9:
13 goes into 30 2 times with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 26585.692
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.

Let's proceed to step 10:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 26585.6923
Subtract 39 from 40 to 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.

Step 11:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 26585.6923
If we subtract 0 from 10, 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.

Advancing to step 12:
13 goes into 100 7 times with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 26585.692307
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.

On to step 13:
90 divided by 13 is 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 26585.6923076
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.

Advancing to step 14:
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: 26585.69230769
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.

In conclusion, the division gives 26585.69230769 with a balance of 3e-09.