We look at the division of 421465 by 13 
We want to divide 421465 by 13.

On to step 1:
13 can be fit into 4 0 times, resulting in a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 13

Moving on to step 2:
If we divide 42 by 13, we get 3 and a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Deduct 39 from 42 and we're left with 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 13

On to step 3:
The number 13 fits into 31 2 times, leaving a remainder of 5.
Record the quotient 2 as the next digit in the result. 
Result so far: 32.0
If we subtract 26 from 31, we get 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 13

On to step 4:
When dividing 54 by 13, we get 4 with a remainder of 2.
Use 4 as the next digit of our solution. 
Result so far: 324.0
Subtracting 52 from 54 leaves us with 2.
Fetch the next digit (6) from the dividend, attach it to 2 and continue: 26 / 13

Let's proceed to step 5:
13 can be fit into 26 2 times, resulting in a remainder of 0.
Use 2 as the next digit of our solution. 
Result so far: 3242.0
Subtract 26 from 26 to get 0.
Append the next digit (5) from the dividend to 0 and continue with: 5 / 13

Moving on to step 6:
5 divided by 13 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 32420.0
If we take 0 away from 5, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 7:
If we divide 50 by 13, we get 3 and a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 32420.3
Deduct 39 from 50 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 8:
The number 13 fits into 110 8 times, leaving a remainder of 6.
The next digit of our result is 8. 
Result so far: 32420.38
If we take 104 away from 110, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 9:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 32420.384
If we take 52 away from 60, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 10:
13 goes into 80 6 times with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 32420.3846
Subtracting 78 from 80 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 11:
When dividing 20 by 13, we get 1 with a remainder of 7.
The next digit of our result is 1. 
Result so far: 32420.38461
Subtracting 13 from 20 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 12:
13 goes into 70 5 times with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 32420.384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 13:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 32420.3846153
Subtracting 39 from 50 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 14:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 32420.38461538
Subtract 104 from 110 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 32420.38461538 and a remainder of 6e-09.