We look at the division of 825713 by 13 
We want to figure out the number of times 825713 can be divided by 13.

Moving on to step 1:
13 goes into 8 0 times with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 13

Let's proceed to step 2:
82 divided by 13 is 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we take 78 away from 82, we end up with 4.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 13

Let's proceed to step 3:
When dividing 45 by 13, we get 3 with a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 63.0
If we subtract 39 from 45, we get 6.
Fetch the next digit (7) from the dividend, attach it to 6 and continue: 67 / 13

Moving on to step 4:
13 can be fit into 67 5 times, resulting in a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 635.0
Deduct 65 from 67 and we're left with 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 13

Step 5:
13 goes into 21 1 times with a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 6351.0
If we take 13 away from 21, we end up with 8.
Grab the next digit (3) from the dividend, add it to 8, then carry on: 83 / 13

Advancing to step 6:
13 goes into 83 6 times with a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 63516.0
Deduct 78 from 83 and we're left with 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 7:
50 divided by 13 is 3 with a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 63516.3
The remainder is 11 after subtracting 39 from 50.
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 8:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 63516.38
If we subtract 104 from 110, we 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.

Moving on to step 9:
The number 13 fits into 60 4 times, leaving a remainder of 8.
The next digit of our result is 4. 
Result so far: 63516.384
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.

Let's proceed to step 10:
When dividing 80 by 13, we get 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 63516.3846
Subtracting 78 from 80 leaves us with 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 11:
13 can be fit into 20 1 times, resulting in a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 63516.38461
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.

Step 12:
When dividing 70 by 13, we get 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 63516.384615
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.

Moving on to step 13:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 63516.3846153
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 14:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 63516.38461538
If we take 104 away from 110, we end up 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.

In conclusion, the division gives 63516.38461538 with a balance of 6e-09.