477617 ÷ 13 
Our goal is to divide 477617 by 13.

Let's proceed to step 1:
13 can be fit into 4 0 times, resulting in a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 13

Let's proceed to step 2:
The number 13 fits into 47 3 times, leaving a remainder of 8.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Subtract 39 from 47 to get 8.
Bring next digit (7) of the dividend behind the 8 and repeat the process: 87 / 13

Going ahead to step 3:
13 goes into 87 6 times with a remainder of 9.
Use 6 as the next digit of our solution. 
Result so far: 36.0
Deduct 78 from 87 and we're left with 9.
Take the next digit (6) from the dividend and append it to 9, then repeat: 96 / 13

Step 4:
13 goes into 96 7 times with a remainder of 5.
Use 7 as the next digit of our solution. 
Result so far: 367.0
Subtracting 91 from 96 leaves us with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 13

Step 5:
13 can be fit into 51 3 times, resulting in a remainder of 12.
Write down 3 as next digit of the result. 
Result so far: 3673.0
Subtract 39 from 51 to get 12.
Grab the next digit (7) from the dividend, add it to 12, then carry on: 127 / 13

Going ahead to step 6:
The number 13 fits into 127 9 times, leaving a remainder of 10.
Put 9 as the next digit of the answer. 
Result so far: 36739.0
If we subtract 117 from 127, we 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.

Advancing to step 7:
13 goes into 100 7 times with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 36739.7
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.

Step 8:
When dividing 90 by 13, we get 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 36739.76
The remainder is 12 after subtracting 78 from 90.
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 9:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 36739.769
If we take 117 away from 120, we end up 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.

Let's proceed to step 10:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 36739.7692
Deduct 26 from 30 and we're left 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.

Going ahead to step 11:
If we divide 40 by 13, we get 3 and a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 36739.76923
If we take 39 away from 40, we end up 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.

Let's proceed to step 12:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 36739.76923
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.

Moving on to step 13:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 36739.7692307
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.

Advancing to step 14:
When dividing 90 by 13, we get 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 36739.76923076
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.

In conclusion, the division gives 36739.76923076 with a balance of 1.2e-08.