680833 ÷ 13 
We're looking to find how many times 13 goes into 680833.

Let's proceed to step 1:
6 divided by 13 is 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 13

Advancing to step 2:
If we divide 68 by 13, we get 5 and a remainder of 3.
The next digit of our result is 5. 
Result so far: 5.0
The remainder is 3 after subtracting 65 from 68.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 13

Step 3:
13 goes into 30 2 times with a remainder of 4.
The next digit of our result is 2. 
Result so far: 52.0
Subtracting 26 from 30 leaves us with 4.
Take the next digit (8) from the dividend and append it to 4, then repeat: 48 / 13

Moving on to step 4:
When dividing 48 by 13, we get 3 with a remainder of 9.
Put 3 as the next digit of the answer. 
Result so far: 523.0
The remainder is 9 after subtracting 39 from 48.
Include the next digit (3) from the dividend after 9, then repeat: 93 / 13

Moving on to step 5:
13 goes into 93 7 times with a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 5237.0
The remainder is 2 after subtracting 91 from 93.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 13

Advancing to step 6:
13 can be fit into 23 1 times, resulting in a remainder of 10.
The next digit of our result is 1. 
Result so far: 52371.0
If we take 13 away from 23, 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.

Moving on to step 7:
When dividing 100 by 13, we get 7 with a remainder of 9.
The next digit of our result is 7. 
Result so far: 52371.7
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.

Moving on to step 8:
90 divided by 13 is 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 52371.76
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 9:
120 divided by 13 is 9 with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 52371.769
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.

Moving on to step 10:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 52371.7692
If we subtract 26 from 30, we get 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:
40 divided by 13 is 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 52371.76923
Deduct 39 from 40 and we're left 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.

Advancing to step 12:
10 divided by 13 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 52371.76923
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.

Step 13:
100 divided by 13 is 7 with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 52371.7692307
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.

Step 14:
13 goes into 90 6 times with a remainder of 12.
The next digit of our result is 6. 
Result so far: 52371.76923076
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.

The final result is 52371.76923076 with a remainder of 1.2e-08.