415458 divided by 13 
We want to divide 415458 by 13.

On to step 1:
If we divide 4 by 13, we get 0 and a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Fetch the next digit (1) from the dividend, attach it to 4 and continue: 41 / 13

Moving on to step 2:
13 can be fit into 41 3 times, resulting in a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 3.0
If we subtract 39 from 41, we get 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 13

Let's proceed to step 3:
25 divided by 13 is 1 with a remainder of 12.
The number 1 becomes the next digit in our result. 
Result so far: 31.0
Subtract 13 from 25 to get 12.
Append the next digit (4) from the dividend to 12 and continue with: 124 / 13

Moving on to step 4:
13 goes into 124 9 times with a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 319.0
If we subtract 117 from 124, we get 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 13

On to step 5:
13 goes into 75 5 times with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 3195.0
Subtract 65 from 75 to get 10.
Grab the next digit (8) from the dividend, add it to 10, then carry on: 108 / 13

Moving on to step 6:
13 can be fit into 108 8 times, resulting in a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 31958.0
The remainder is 4 after subtracting 104 from 108.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 31958.3
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.

Going ahead to step 8:
If we divide 10 by 13, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 31958.3
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:
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: 31958.307
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.

Moving on to step 10:
13 goes into 90 6 times with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 31958.3076
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.

Advancing to step 11:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 31958.30769
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.

Advancing to step 12:
30 divided by 13 is 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 31958.307692
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.

Going ahead to step 13:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 31958.3076923
If we subtract 39 from 40, we 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 14:
When dividing 10 by 13, we get 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 31958.3076923
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.

In conclusion, the division gives 31958.3076923 with a balance of 1e-08.