Let's divide 434126 by 13
We want to divide 434126 by 13.

On to step 1:
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: 0.0
If we take 0 away from 4, we end up with 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 13

Moving on to step 2:
When dividing 43 by 13, we get 3 with a remainder of 4.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we subtract 39 from 43, we get 4.
Include the next digit (4) from the dividend after 4, then repeat: 44 / 13

Let's proceed to step 3:
13 can be fit into 44 3 times, resulting in a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 33.0
Subtracting 39 from 44 leaves us with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 13

Advancing to step 4:
13 goes into 51 3 times with a remainder of 12.
Use 3 as the next digit of our solution. 
Result so far: 333.0
Deduct 39 from 51 and we're left with 12.
Bring next digit (2) of the dividend behind the 12 and repeat the process: 122 / 13

Going ahead to step 5:
122 divided by 13 is 9 with a remainder of 5.
Put 9 as the next digit of the answer. 
Result so far: 3339.0
Subtracting 117 from 122 leaves us with 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 13

Moving on to step 6:
When dividing 56 by 13, we get 4 with a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 33394.0
Deduct 52 from 56 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 7:
13 goes into 40 3 times with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 33394.3
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.

Let's proceed to step 8:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 33394.3
Deduct 0 from 10 and we're left 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.

Going ahead to step 9:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 33394.307
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 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: 33394.3076
Deduct 78 from 90 and we're left 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:
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: 33394.30769
Deduct 117 from 120 and we're left 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.

On to step 12:
13 goes into 30 2 times with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 33394.307692
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.

On to step 13:
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: 33394.3076923
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.

Step 14:
10 divided by 13 is 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 33394.3076923
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 33394.3076923 with a balance of 1e-08.