We look at the division of 825635 by 13 
We want to figure out the number of times 825635 can be divided by 13.

Advancing to step 1:
If we divide 8 by 13, we get 0 and a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 13

Going ahead to step 2:
13 can be fit into 82 6 times, resulting in a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Subtracting 78 from 82 leaves us with 4.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 13

Going ahead to step 3:
45 divided by 13 is 3 with a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 63.0
Subtract 39 from 45 to get 6.
Fetch the next digit (6) from the dividend, attach it to 6 and continue: 66 / 13

Advancing to step 4:
The number 13 fits into 66 5 times, leaving a remainder of 1.
Put 5 as the next digit of the answer. 
Result so far: 635.0
If we subtract 65 from 66, we get 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 13

Going ahead to step 5:
The number 13 fits into 13 1 times, leaving a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 6351.0
Subtracting 13 from 13 leaves us with 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 13

Step 6:
5 divided by 13 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 63510.0
If we take 0 away from 5, we end up 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:
The number 13 fits into 50 3 times, leaving a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 63510.3
Subtracting 39 from 50 leaves us 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.

Moving on to step 8:
If we divide 110 by 13, we get 8 and a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 63510.38
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.

On to step 9:
The number 13 fits into 60 4 times, leaving a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 63510.384
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.

Step 10:
80 divided by 13 is 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 63510.3846
If we take 78 away from 80, we end up 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:
20 divided by 13 is 1 with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 63510.38461
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.

Moving on to step 12:
If we divide 70 by 13, we get 5 and a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 63510.384615
If we take 65 away from 70, we end up 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 13:
50 divided by 13 is 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 63510.3846153
Deduct 39 from 50 and we're left 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:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 63510.38461538
The remainder is 6 after subtracting 104 from 110.
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 63510.38461538 with a balance of 6e-09.