683431 divided by 13 
We want to figure out the number of times 683431 can be divided by 13.

Step 1:
When dividing 6 by 13, we get 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 13

On to step 2:
13 goes into 68 5 times with a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 5.0
If we subtract 65 from 68, we get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 13

Moving on to step 3:
13 can be fit into 33 2 times, resulting in a remainder of 7.
The next digit of our result is 2. 
Result so far: 52.0
The remainder is 7 after subtracting 26 from 33.
Bring next digit (4) of the dividend behind the 7 and repeat the process: 74 / 13

On to step 4:
The number 13 fits into 74 5 times, leaving a remainder of 9.
The next digit of our result is 5. 
Result so far: 525.0
If we take 65 away from 74, we end up with 9.
Fetch the next digit (3) from the dividend, attach it to 9 and continue: 93 / 13

Advancing to step 5:
13 can be fit into 93 7 times, resulting in a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 5257.0
Subtract 91 from 93 to get 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 13

Let's proceed to step 6:
If we divide 21 by 13, we get 1 and a remainder of 8.
Put 1 as the next digit of the answer. 
Result so far: 52571.0
If we subtract 13 from 21, we get 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 7:
When dividing 80 by 13, we get 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 52571.6
The remainder is 2 after subtracting 78 from 80.
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 8:
If we divide 20 by 13, we get 1 and a remainder of 7.
The next digit of our result is 1. 
Result so far: 52571.61
Deduct 13 from 20 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 9:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 52571.615
Subtract 65 from 70 to 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.

Going ahead to step 10:
When dividing 50 by 13, we get 3 with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 52571.6153
If we take 39 away from 50, we end up with 11.
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 11:
When dividing 110 by 13, we get 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 52571.61538
Subtracting 104 from 110 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 12:
When dividing 60 by 13, we get 4 with a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 52571.615384
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.

Advancing to step 13:
If we divide 80 by 13, we get 6 and a remainder of 2.
The next digit of our result is 6. 
Result so far: 52571.6153846
Subtract 78 from 80 to 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.

Advancing to step 14:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 52571.61538461
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The final result is 52571.61538461 with a remainder of 7e-09.