459636 ÷ 13 
Our goal is to divide 459636 by 13.

Going ahead to step 1:
When dividing 4 by 13, we get 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 13

Let's proceed to step 2:
If we divide 45 by 13, we get 3 and a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Subtract 39 from 45 to get 6.
Grab the next digit (9) from the dividend, add it to 6, then carry on: 69 / 13

Let's proceed to step 3:
The number 13 fits into 69 5 times, leaving a remainder of 4.
Put 5 as the next digit of the answer. 
Result so far: 35.0
Subtracting 65 from 69 leaves us with 4.
Grab the next digit (6) from the dividend, add it to 4, then carry on: 46 / 13

Moving on to step 4:
The number 13 fits into 46 3 times, leaving a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 353.0
Deduct 39 from 46 and we're left with 7.
Fetch the next digit (3) from the dividend, attach it to 7 and continue: 73 / 13

Advancing to step 5:
When dividing 73 by 13, we get 5 with a remainder of 8.
Record the quotient 5 as the next digit in the result. 
Result so far: 3535.0
Subtracting 65 from 73 leaves us with 8.
Bring next digit (6) of the dividend behind the 8 and repeat the process: 86 / 13

Advancing to step 6:
If we divide 86 by 13, we get 6 and a remainder of 8.
The next digit of our result is 6. 
Result so far: 35356.0
Subtracting 78 from 86 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 7:
80 divided by 13 is 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 35356.6
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.

Step 8:
13 goes into 20 1 times with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 35356.61
If we take 13 away from 20, we end up 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.

On to step 9:
70 divided by 13 is 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 35356.615
Deduct 65 from 70 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.

Moving on to step 10:
If we divide 50 by 13, we get 3 and a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 35356.6153
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.

On to step 11:
110 divided by 13 is 8 with a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 35356.61538
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.

Going ahead to step 12:
If we divide 60 by 13, we get 4 and a remainder of 8.
The next digit of our result is 4. 
Result so far: 35356.615384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 13:
80 divided by 13 is 6 with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 35356.6153846
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.

Let's proceed to step 14:
13 goes into 20 1 times with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 35356.61538461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

In conclusion, the division gives 35356.61538461 with a balance of 7e-09.