We're dividing 636598 by 13 
We're looking to find how many times 13 goes into 636598.

Advancing to step 1:
13 can be fit into 6 0 times, resulting in a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (3) from the dividend to 6 and continue with: 63 / 13

Let's proceed to step 2:
63 divided by 13 is 4 with a remainder of 11.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtracting 52 from 63 leaves us with 11.
Include the next digit (6) from the dividend after 11, then repeat: 116 / 13

Let's proceed to step 3:
13 can be fit into 116 8 times, resulting in a remainder of 12.
The next digit of our result is 8. 
Result so far: 48.0
If we take 104 away from 116, we end up with 12.
Append the next digit (5) from the dividend to 12 and continue with: 125 / 13

Step 4:
The number 13 fits into 125 9 times, leaving a remainder of 8.
Put 9 as the next digit of the answer. 
Result so far: 489.0
Subtract 117 from 125 to get 8.
Include the next digit (9) from the dividend after 8, then repeat: 89 / 13

On to step 5:
13 goes into 89 6 times with a remainder of 11.
The next digit of our result is 6. 
Result so far: 4896.0
Deduct 78 from 89 and we're left with 11.
Take the next digit (8) from the dividend and append it to 11, then repeat: 118 / 13

Let's proceed to step 6:
13 goes into 118 9 times with a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 48969.0
The remainder is 1 after subtracting 117 from 118.
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 7:
If we divide 10 by 13, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 48969.0
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.

Let's proceed to step 8:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 48969.07
The remainder is 9 after subtracting 91 from 100.
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 9:
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: 48969.076
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.

Let's proceed to step 10:
When dividing 120 by 13, we get 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 48969.0769
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.

Going ahead to step 11:
When dividing 30 by 13, we get 2 with a remainder of 4.
The next digit of our result is 2. 
Result so far: 48969.07692
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.

Moving on to step 12:
When dividing 40 by 13, we get 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 48969.076923
Subtracting 39 from 40 leaves us 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.

Moving on to step 13:
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: 48969.076923
If we take 0 away from 10, we end up 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.

Let's proceed to step 14:
13 can be fit into 100 7 times, resulting in a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 48969.07692307
Deduct 91 from 100 and we're left 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.

The final result is 48969.07692307 with a remainder of 9e-09.