We look at the division of 683413 by 13 
We want to figure out the number of times 683413 can be divided by 13.

Moving on to step 1:
13 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Append the next digit (8) from the dividend to 6 and continue with: 68 / 13

Going ahead to step 2:
68 divided by 13 is 5 with a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 5.0
The remainder is 3 after subtracting 65 from 68.
Include the next digit (3) from the dividend after 3, then repeat: 33 / 13

Advancing to step 3:
When dividing 33 by 13, we get 2 with a remainder of 7.
Use 2 as the next digit of our solution. 
Result so far: 52.0
If we subtract 26 from 33, we get 7.
Grab the next digit (4) from the dividend, add it to 7, then carry on: 74 / 13

On to step 4:
When dividing 74 by 13, we get 5 with a remainder of 9.
The number 5 becomes the next digit in our result. 
Result so far: 525.0
Subtract 65 from 74 to get 9.
Fetch the next digit (1) from the dividend, attach it to 9 and continue: 91 / 13

Advancing to step 5:
13 can be fit into 91 7 times, resulting in a remainder of 0.
The number 7 becomes the next digit in our result. 
Result so far: 5257.0
If we take 91 away from 91, we end up with 0.
Grab the next digit (3) from the dividend, add it to 0, then carry on: 3 / 13

Let's proceed to step 6:
If we divide 3 by 13, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 52570.0
If we take 0 away from 3, 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 7:
13 goes into 30 2 times with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 52570.2
If we take 26 away from 30, we end up 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.

Moving on to step 8:
13 can be fit into 40 3 times, resulting in a remainder of 1.
The next digit of our result is 3. 
Result so far: 52570.23
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.

Advancing to step 9:
When dividing 10 by 13, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 52570.23
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.

Step 10:
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: 52570.2307
If we take 91 away from 100, we end up 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.

Moving on to step 11:
90 divided by 13 is 6 with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 52570.23076
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.

On to step 12:
The number 13 fits into 120 9 times, leaving a remainder of 3.
The next digit of our result is 9. 
Result so far: 52570.230769
Subtracting 117 from 120 leaves us 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 13:
When dividing 30 by 13, we get 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 52570.2307692
If we subtract 26 from 30, we 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.

Let's proceed to step 14:
40 divided by 13 is 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 52570.23076923
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.

The quotient of the division is 52570.23076923, and the remainder is 1e-09.