Let's divide 434435 by 13
We want to figure out the number of times 434435 can be divided by 13.

On to step 1:
If we divide 4 by 13, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 13

Going ahead to step 2:
When dividing 43 by 13, we get 3 with a remainder of 4.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we take 39 away from 43, we end up with 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 13

Step 3:
When dividing 44 by 13, we get 3 with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 33.0
Deduct 39 from 44 and we're left with 5.
Fetch the next digit (4) from the dividend, attach it to 5 and continue: 54 / 13

Let's proceed to step 4:
13 can be fit into 54 4 times, resulting in a remainder of 2.
The next digit of our result is 4. 
Result so far: 334.0
The remainder is 2 after subtracting 52 from 54.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 13

Step 5:
13 goes into 23 1 times with a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 3341.0
Subtracting 13 from 23 leaves us with 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 13

Moving on to step 6:
13 can be fit into 105 8 times, resulting in a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 33418.0
Subtract 104 from 105 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.

Step 7:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 33418.0
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.

Let's proceed to step 8:
The number 13 fits into 100 7 times, leaving a remainder of 9.
The next digit of our result is 7. 
Result so far: 33418.07
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.

Advancing to step 9:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 33418.076
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 10:
When dividing 120 by 13, we get 9 with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 33418.0769
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.

Advancing to step 11:
If we divide 30 by 13, we get 2 and a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 33418.07692
If we take 26 away from 30, we end up 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.

Step 12:
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: 33418.076923
Deduct 39 from 40 and we're left 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 13:
13 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 33418.076923
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.

Advancing to step 14:
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: 33418.07692307
Subtract 91 from 100 to 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.

The quotient of the division is 33418.07692307, and the remainder is 9e-09.