357317 ÷ 13 
We want to divide 357317 by 13.

Going ahead to step 1:
3 divided by 13 is 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 13

Moving on to step 2:
The number 13 fits into 35 2 times, leaving a remainder of 9.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtract 26 from 35 to get 9.
Include the next digit (7) from the dividend after 9, then repeat: 97 / 13

On to step 3:
13 goes into 97 7 times with a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 27.0
Deduct 91 from 97 and we're left with 6.
Include the next digit (3) from the dividend after 6, then repeat: 63 / 13

Going ahead to step 4:
13 can be fit into 63 4 times, resulting in a remainder of 11.
Use 4 as the next digit of our solution. 
Result so far: 274.0
Subtract 52 from 63 to get 11.
Append the next digit (1) from the dividend to 11 and continue with: 111 / 13

Going ahead to step 5:
When dividing 111 by 13, we get 8 with a remainder of 7.
Use 8 as the next digit of our solution. 
Result so far: 2748.0
Subtracting 104 from 111 leaves us with 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 13

On to step 6:
77 divided by 13 is 5 with a remainder of 12.
Use 5 as the next digit of our solution. 
Result so far: 27485.0
If we take 65 away from 77, 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.

Moving on to step 7:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 27485.9
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.

Let's proceed to step 8:
13 goes into 30 2 times with a remainder of 4.
The next digit of our result is 2. 
Result so far: 27485.92
If we subtract 26 from 30, we get 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 9:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 27485.923
Subtract 39 from 40 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 10:
10 divided by 13 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 27485.923
If we subtract 0 from 10, 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.

Moving on to step 11:
If we divide 100 by 13, we get 7 and a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 27485.92307
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.

Let's proceed to step 12:
90 divided by 13 is 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 27485.923076
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.

Step 13:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 27485.9230769
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.

Advancing to step 14:
13 goes into 30 2 times with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 27485.92307692
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.

In conclusion, the division gives 27485.92307692 with a balance of 4e-09.