829266 ÷ 13 
We're looking to find how many times 13 goes into 829266.

Let's proceed to step 1:
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: 0.0
Subtract 0 from 8 to get 8.
Append the next digit (2) from the dividend to 8 and continue with: 82 / 13

Let's proceed to step 2:
If we divide 82 by 13, we get 6 and a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 78 away from 82, we end up with 4.
Include the next digit (9) from the dividend after 4, then repeat: 49 / 13

Let's proceed to step 3:
When dividing 49 by 13, we get 3 with a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 63.0
Subtracting 39 from 49 leaves us with 10.
Grab the next digit (2) from the dividend, add it to 10, then carry on: 102 / 13

Going ahead to step 4:
102 divided by 13 is 7 with a remainder of 11.
Put 7 as the next digit of the answer. 
Result so far: 637.0
Deduct 91 from 102 and we're left with 11.
Append the next digit (6) from the dividend to 11 and continue with: 116 / 13

Going ahead to step 5:
13 goes into 116 8 times with a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 6378.0
Deduct 104 from 116 and we're left with 12.
Bring next digit (6) of the dividend behind the 12 and repeat the process: 126 / 13

On to step 6:
If we divide 126 by 13, we get 9 and a remainder of 9.
The number 9 becomes the next digit in our result. 
Result so far: 63789.0
The remainder is 9 after subtracting 117 from 126.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 7:
13 goes into 90 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 63789.6
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.

Let's proceed to step 8:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 63789.69
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.

Moving on to step 9:
When dividing 30 by 13, we get 2 with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 63789.692
Deduct 26 from 30 and we're left 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.

Going ahead to step 10:
13 can be fit into 40 3 times, resulting in a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 63789.6923
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:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 63789.6923
Subtract 0 from 10 to 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.

Moving on to step 12:
The number 13 fits into 100 7 times, leaving a remainder of 9.
The next digit of our result is 7. 
Result so far: 63789.692307
Subtract 91 from 100 to 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 13:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 63789.6923076
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.

Moving on to step 14:
If we divide 120 by 13, we get 9 and a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 63789.69230769
The remainder is 3 after subtracting 117 from 120.
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 63789.69230769 with a balance of 3e-09.