832105 ÷ 13 
Our goal is to divide 832105 by 13.

Step 1:
13 goes into 8 0 times with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Append the next digit (3) from the dividend to 8 and continue with: 83 / 13

Going ahead to step 2:
13 goes into 83 6 times with a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Deduct 78 from 83 and we're left with 5.
Append the next digit (2) from the dividend to 5 and continue with: 52 / 13

On to step 3:
13 can be fit into 52 4 times, resulting in a remainder of 0.
The next digit of our result is 4. 
Result so far: 64.0
If we take 52 away from 52, we end up with 0.
Fetch the next digit (1) from the dividend, attach it to 0 and continue: 1 / 13

Advancing to step 4:
When dividing 1 by 13, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 640.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 13

Let's proceed to step 5:
The number 13 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 6400.0
Subtracting 0 from 10 leaves us with 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 13

Moving on to step 6:
13 can be fit into 105 8 times, resulting in a remainder of 1.
Use 8 as the next digit of our solution. 
Result so far: 64008.0
The remainder is 1 after subtracting 104 from 105.
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 7:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 64008.0
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.

On to step 8:
13 goes into 100 7 times with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 64008.07
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.

On to step 9:
13 goes into 90 6 times with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 64008.076
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.

Moving on to step 10:
When dividing 120 by 13, we get 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 64008.0769
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 11:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 64008.07692
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.

Step 12:
When dividing 40 by 13, we get 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 64008.076923
If we subtract 39 from 40, we 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 13:
If we divide 10 by 13, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 64008.076923
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.

On to step 14:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 64008.07692307
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.

Our division results in 64008.07692307 with a remaining 9e-09.