We divide 682512 by 13
We're looking to find how many times 13 goes into 682512.

Step 1:
If we divide 6 by 13, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (8) from the dividend after 6, then repeat: 68 / 13

Let's proceed to step 2:
13 can be fit into 68 5 times, resulting in 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.
Include the next digit (2) from the dividend after 3, then repeat: 32 / 13

Moving on to step 3:
32 divided by 13 is 2 with a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 52.0
Subtracting 26 from 32 leaves us with 6.
Take the next digit (5) from the dividend and append it to 6, then repeat: 65 / 13

Going ahead to step 4:
13 goes into 65 5 times with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 525.0
Deduct 65 from 65 and we're left with 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 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: 5250.0
If we subtract 0 from 1, we get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 13

Step 6:
If we divide 12 by 13, we get 0 and a remainder of 12.
Write down 0 as next digit of the result. 
Result so far: 52500.0
Subtracting 0 from 12 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 7:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 52500.9
If we subtract 117 from 120, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 8:
30 divided by 13 is 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 52500.92
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.

Let's proceed to step 9:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The next digit of our result is 3. 
Result so far: 52500.923
Subtract 39 from 40 to 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.

On to step 10:
13 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 52500.923
Deduct 0 from 10 and we're left 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.

Advancing to step 11:
If we divide 100 by 13, we get 7 and a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 52500.92307
Subtract 91 from 100 to 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.

Advancing to step 12:
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: 52500.923076
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 13:
When dividing 120 by 13, we get 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 52500.9230769
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.

Moving on to step 14:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 52500.92307692
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.

The final result is 52500.92307692 with a remainder of 4e-09.