We're dividing 478903 by 13 
We're looking to find how many times 13 goes into 478903.

Moving on to step 1:
The number 13 fits into 4 0 times, leaving a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Include the next digit (7) from the dividend after 4, then repeat: 47 / 13

Advancing to step 2:
If we divide 47 by 13, we get 3 and a remainder of 8.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we take 39 away from 47, we end up with 8.
Include the next digit (8) from the dividend after 8, then repeat: 88 / 13

Step 3:
The number 13 fits into 88 6 times, leaving a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 36.0
If we subtract 78 from 88, we get 10.
Bring next digit (9) of the dividend behind the 10 and repeat the process: 109 / 13

On to step 4:
13 can be fit into 109 8 times, resulting in a remainder of 5.
Write down 8 as next digit of the result. 
Result so far: 368.0
If we subtract 104 from 109, we get 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 13

Let's proceed to step 5:
If we divide 50 by 13, we get 3 and a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 3683.0
If we take 39 away from 50, we end up with 11.
Fetch the next digit (3) from the dividend, attach it to 11 and continue: 113 / 13

Moving on to step 6:
13 goes into 113 8 times with a remainder of 9.
Use 8 as the next digit of our solution. 
Result so far: 36838.0
If we take 104 away from 113, we end up 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.

Step 7:
13 can be fit into 90 6 times, resulting in a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 36838.6
If we take 78 away from 90, we end up 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 8:
If we divide 120 by 13, we get 9 and a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 36838.69
Subtracting 117 from 120 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 9:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 36838.692
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 10:
40 divided by 13 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 36838.6923
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.

Advancing to step 11:
10 divided by 13 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 36838.6923
Subtract 0 from 10 to get 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 12:
13 goes into 100 7 times with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 36838.692307
Subtracting 91 from 100 leaves us 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.

Going ahead to step 13:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 36838.6923076
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.

On to step 14:
If we divide 120 by 13, we get 9 and a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 36838.69230769
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.

After the division, we end up with 36838.69230769 and a remainder of 3e-09.