410817 ÷ 13 
Let's see how many times 13 fits into 410817.

Step 1:
When dividing 4 by 13, we get 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 13

Moving on to step 2:
If we divide 41 by 13, we get 3 and a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 3.0
Subtracting 39 from 41 leaves us with 2.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 13

On to step 3:
20 divided by 13 is 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 31.0
Subtract 13 from 20 to get 7.
Append the next digit (8) from the dividend to 7 and continue with: 78 / 13

Step 4:
13 goes into 78 6 times with a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 316.0
If we take 78 away from 78, we end up with 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 13

Going ahead to step 5:
13 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 3160.0
If we subtract 0 from 1, we get 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 13

Let's proceed to step 6:
If we divide 17 by 13, we get 1 and a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 31601.0
Deduct 13 from 17 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 7:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 31601.3
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.

Step 8:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 31601.3
If we subtract 0 from 10, we 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.

Going ahead to step 9:
13 goes into 100 7 times with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 31601.307
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.

Step 10:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The next digit of our result is 6. 
Result so far: 31601.3076
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 11:
If we divide 120 by 13, we get 9 and a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 31601.30769
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.

Advancing to step 12:
13 can be fit into 30 2 times, resulting in a remainder of 4.
The next digit of our result is 2. 
Result so far: 31601.307692
Subtract 26 from 30 to 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 13:
13 goes into 40 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 31601.3076923
If we take 39 away from 40, we end up 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.

Moving on to step 14:
10 divided by 13 is 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 31601.3076923
If we subtract 0 from 10, we 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.

In conclusion, the division gives 31601.3076923 with a balance of 1e-08.