We're dividing 814435 by 13 
We want to divide 814435 by 13.

Step 1:
When dividing 8 by 13, we get 0 with a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Append the next digit (1) from the dividend to 8 and continue with: 81 / 13

Moving on to step 2:
13 can be fit into 81 6 times, resulting in a remainder of 3.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 3 after subtracting 78 from 81.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 13

Advancing to step 3:
34 divided by 13 is 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 62.0
Deduct 26 from 34 and we're left with 8.
Take the next digit (4) from the dividend and append it to 8, then repeat: 84 / 13

On to step 4:
84 divided by 13 is 6 with a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 626.0
Subtract 78 from 84 to get 6.
Include the next digit (3) from the dividend after 6, then repeat: 63 / 13

Going ahead to step 5:
If we divide 63 by 13, we get 4 and a remainder of 11.
Write down 4 as next digit of the result. 
Result so far: 6264.0
If we subtract 52 from 63, we get 11.
Take the next digit (5) from the dividend and append it to 11, then repeat: 115 / 13

Moving on to step 6:
13 can be fit into 115 8 times, resulting in a remainder of 11.
The next digit of our result is 8. 
Result so far: 62648.0
The remainder is 11 after subtracting 104 from 115.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 7:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 62648.8
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 8:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 62648.84
Subtracting 52 from 60 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 9:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 62648.846
If we subtract 78 from 80, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 10:
When dividing 20 by 13, we get 1 with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 62648.8461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 11:
When dividing 70 by 13, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 62648.84615
If we subtract 65 from 70, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 12:
When dividing 50 by 13, we get 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 62648.846153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 13:
When dividing 110 by 13, we get 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 62648.8461538
Subtract 104 from 110 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 14:
When dividing 60 by 13, we get 4 with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 62648.84615384
Deduct 52 from 60 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The quotient of the division is 62648.84615384, and the remainder is 8e-09.