We divide 402568 by 13
We want to figure out the number of times 402568 can be divided by 13.

Going ahead to step 1:
When dividing 4 by 13, we get 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 13

Advancing to step 2:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 1 after subtracting 39 from 40.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 13

Let's proceed to step 3:
When dividing 12 by 13, we get 0 with a remainder of 12.
Use 0 as the next digit of our solution. 
Result so far: 30.0
If we subtract 0 from 12, we get 12.
Take the next digit (5) from the dividend and append it to 12, then repeat: 125 / 13

Going ahead to step 4:
The number 13 fits into 125 9 times, leaving a remainder of 8.
Put 9 as the next digit of the answer. 
Result so far: 309.0
Subtracting 117 from 125 leaves us with 8.
Grab the next digit (6) from the dividend, add it to 8, then carry on: 86 / 13

Let's proceed to step 5:
13 goes into 86 6 times with a remainder of 8.
The number 6 becomes the next digit in our result. 
Result so far: 3096.0
If we subtract 78 from 86, we get 8.
Include the next digit (8) from the dividend after 8, then repeat: 88 / 13

On to step 6:
If we divide 88 by 13, we get 6 and a remainder of 10.
The next digit of our result is 6. 
Result so far: 30966.0
Subtract 78 from 88 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 7:
13 goes into 100 7 times with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 30966.7
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 8:
If we divide 90 by 13, we get 6 and a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 30966.76
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.

Moving on to step 9:
120 divided by 13 is 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 30966.769
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.

On to step 10:
When dividing 30 by 13, we get 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 30966.7692
Subtracting 26 from 30 leaves us 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.

On to step 11:
If we divide 40 by 13, we get 3 and a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 30966.76923
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.

Moving on to step 12:
13 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 30966.76923
The remainder is 10 after subtracting 0 from 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 13:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 30966.7692307
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.

Let's proceed to step 14:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 30966.76923076
Deduct 78 from 90 and we're left 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.

The final result is 30966.76923076 with a remainder of 1.2e-08.