We're dividing 208842 by 13 
We're looking to find how many times 13 goes into 208842.

Step 1:
13 goes into 2 0 times with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (0) from the dividend to 2 and continue with: 20 / 13

Let's proceed to step 2:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 13 from 20, we get 7.
Include the next digit (8) from the dividend after 7, then repeat: 78 / 13

Advancing to step 3:
13 can be fit into 78 6 times, resulting in a remainder of 0.
The number 6 becomes the next digit in our result. 
Result so far: 16.0
The remainder is 0 after subtracting 78 from 78.
Include the next digit (8) from the dividend after 0, then repeat: 8 / 13

On to step 4:
If we divide 8 by 13, we get 0 and a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 160.0
The remainder is 8 after subtracting 0 from 8.
Take the next digit (4) from the dividend and append it to 8, then repeat: 84 / 13

Moving on to step 5:
13 can be fit into 84 6 times, resulting in a remainder of 6.
The number 6 becomes the next digit in our result. 
Result so far: 1606.0
Deduct 78 from 84 and we're left with 6.
Append the next digit (2) from the dividend to 6 and continue with: 62 / 13

Advancing to step 6:
62 divided by 13 is 4 with a remainder of 10.
The next digit of our result is 4. 
Result so far: 16064.0
Deduct 52 from 62 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 7:
If we divide 100 by 13, we get 7 and a remainder of 9.
The next digit of our result is 7. 
Result so far: 16064.7
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.

Going ahead to step 8:
If we divide 90 by 13, we get 6 and a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 16064.76
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.

Step 9:
13 goes into 120 9 times with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 16064.769
Subtract 117 from 120 to 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.

Going ahead to step 10:
The number 13 fits into 30 2 times, leaving a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 16064.7692
If we take 26 away from 30, we end up 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.

Step 11:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 16064.76923
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 12:
13 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 16064.76923
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 13:
When dividing 100 by 13, we get 7 with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 16064.7692307
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.

On to step 14:
90 divided by 13 is 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 16064.76923076
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.

In conclusion, the division gives 16064.76923076 with a balance of 1.2e-08.