We look at the division of 338594 by 13 
We're looking to find how many times 13 goes into 338594.

On to step 1:
If we divide 3 by 13, we get 0 and a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 13

Going ahead to step 2:
If we divide 33 by 13, we get 2 and a remainder of 7.
Put 2 as the next digit of the answer. 
Result so far: 2.0
If we subtract 26 from 33, we get 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 13

Step 3:
If we divide 78 by 13, we get 6 and a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 26.0
Deduct 78 from 78 and we're left with 0.
Fetch the next digit (5) from the dividend, attach it to 0 and continue: 5 / 13

Step 4:
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: 260.0
The remainder is 5 after subtracting 0 from 5.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 13

On to step 5:
If we divide 59 by 13, we get 4 and a remainder of 7.
Record the quotient 4 as the next digit in the result. 
Result so far: 2604.0
Deduct 52 from 59 and we're left with 7.
Take the next digit (4) from the dividend and append it to 7, then repeat: 74 / 13

Going ahead to step 6:
If we divide 74 by 13, we get 5 and a remainder of 9.
Put 5 as the next digit of the answer. 
Result so far: 26045.0
Deduct 65 from 74 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.

On to step 7:
When dividing 90 by 13, we get 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 26045.6
Subtracting 78 from 90 leaves us 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 8:
13 goes into 120 9 times with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 26045.69
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.

Moving on to step 9:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 26045.692
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.

On to step 10:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 26045.6923
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.

On to step 11:
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: 26045.6923
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.

Moving on to step 12:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 26045.692307
Subtracting 91 from 100 leaves us 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:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 26045.6923076
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.

Step 14:
13 goes into 120 9 times with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 26045.69230769
If we subtract 117 from 120, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The final result is 26045.69230769 with a remainder of 3e-09.