We look at the division of 421695 by 13 
Let's see how many times 13 fits into 421695.

On to step 1:
13 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 13

Let's proceed to step 2:
13 can be fit into 42 3 times, resulting in a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 3 after subtracting 39 from 42.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 13

Let's proceed to step 3:
If we divide 31 by 13, we get 2 and a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 32.0
The remainder is 5 after subtracting 26 from 31.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 13

On to step 4:
If we divide 56 by 13, we get 4 and a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 324.0
The remainder is 4 after subtracting 52 from 56.
Fetch the next digit (9) from the dividend, attach it to 4 and continue: 49 / 13

On to step 5:
13 can be fit into 49 3 times, resulting in a remainder of 10.
The next digit of our result is 3. 
Result so far: 3243.0
Deduct 39 from 49 and we're left with 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 13

Let's proceed to step 6:
When dividing 105 by 13, we get 8 with a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 32438.0
If we subtract 104 from 105, 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 7:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 32438.0
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:
13 goes into 100 7 times with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 32438.07
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.

Let's proceed to step 9:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 32438.076
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.

Going ahead to step 10:
120 divided by 13 is 9 with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 32438.0769
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.

Step 11:
When dividing 30 by 13, we get 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 32438.07692
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.

On to step 12:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 32438.076923
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.

Moving on to step 13:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 32438.076923
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.

Moving on to step 14:
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: 32438.07692307
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.

Our division results in 32438.07692307 with a remaining 9e-09.