We're dividing 421648 by 13 
We want to figure out the number of times 421648 can be divided by 13.

Advancing to step 1:
13 goes into 4 0 times 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.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 13

Advancing to step 2:
The number 13 fits into 42 3 times, leaving a remainder of 3.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 3 after subtracting 39 from 42.
Include the next digit (1) from the dividend after 3, then repeat: 31 / 13

Moving 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.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 13

Advancing 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
Subtract 52 from 56 to get 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 13

Step 5:
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: 3243.0
If we subtract 39 from 44, we get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 13

Going ahead to step 6:
The number 13 fits into 58 4 times, leaving a remainder of 6.
The next digit of our result is 4. 
Result so far: 32434.0
Deduct 52 from 58 and we're left 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.

Going ahead to step 7:
60 divided by 13 is 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 32434.4
Subtracting 52 from 60 leaves us 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.

Moving on to step 8:
80 divided by 13 is 6 with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 32434.46
Subtract 78 from 80 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 9:
13 goes into 20 1 times with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 32434.461
Deduct 13 from 20 and we're left 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.

Moving on to step 10:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 32434.4615
If we subtract 65 from 70, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 11:
When dividing 50 by 13, we get 3 with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 32434.46153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 12:
13 can be fit into 110 8 times, resulting in a remainder of 6.
The next digit of our result is 8. 
Result so far: 32434.461538
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 13:
When dividing 60 by 13, we get 4 with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 32434.4615384
Deduct 52 from 60 and we're left 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.

Advancing to step 14:
When dividing 80 by 13, we get 6 with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 32434.46153846
Subtract 78 from 80 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 32434.46153846, and the remainder is 2e-09.