557834 ÷ 13 
We're looking to find how many times 13 goes into 557834.

Advancing to step 1:
13 can be fit into 5 0 times, resulting in a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 13

Moving on to step 2:
13 can be fit into 55 4 times, resulting in a remainder of 3.
Write down 4 as next digit of the result. 
Result so far: 4.0
Deduct 52 from 55 and we're left with 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 13

Step 3:
13 goes into 37 2 times with a remainder of 11.
Write down 2 as next digit of the result. 
Result so far: 42.0
If we subtract 26 from 37, we get 11.
Fetch the next digit (8) from the dividend, attach it to 11 and continue: 118 / 13

On to step 4:
13 goes into 118 9 times with a remainder of 1.
The next digit of our result is 9. 
Result so far: 429.0
The remainder is 1 after subtracting 117 from 118.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 13

Moving on to step 5:
The number 13 fits into 13 1 times, leaving a remainder of 0.
Write down 1 as next digit of the result. 
Result so far: 4291.0
If we take 13 away from 13, we end up with 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 13

Advancing to step 6:
When dividing 4 by 13, we get 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 42910.0
The remainder is 4 after subtracting 0 from 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
40 divided by 13 is 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 42910.3
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.

On to step 8:
13 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 42910.3
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 9:
13 goes into 100 7 times with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 42910.307
If we subtract 91 from 100, we get 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 10:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 42910.3076
Subtract 78 from 90 to get 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 11:
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: 42910.30769
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.

Moving on to step 12:
13 goes into 30 2 times with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 42910.307692
Subtract 26 from 30 to 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.

Step 13:
When dividing 40 by 13, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 42910.3076923
The remainder is 1 after subtracting 39 from 40.
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 14:
10 divided by 13 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 42910.3076923
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Our division results in 42910.3076923 with a remaining 1e-08.