We're dividing 420213 by 13 
We want to figure out the number of times 420213 can be divided by 13.

Let's proceed to step 1:
13 can be fit into 4 0 times, resulting in a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 13

Advancing to step 2:
When dividing 42 by 13, we get 3 with a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 3.0
The remainder is 3 after subtracting 39 from 42.
Take the next digit (0) from the dividend and append it to 3, then repeat: 30 / 13

Step 3:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 32.0
If we subtract 26 from 30, we get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 13

Step 4:
42 divided by 13 is 3 with a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 323.0
Subtracting 39 from 42 leaves us with 3.
Take the next digit (1) from the dividend and append it to 3, then repeat: 31 / 13

Moving on to step 5:
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: 3232.0
If we subtract 26 from 31, we get 5.
Take the next digit (3) from the dividend and append it to 5, then repeat: 53 / 13

Let's proceed to step 6:
13 can be fit into 53 4 times, resulting in a remainder of 1.
Record the quotient 4 as the next digit in the result. 
Result so far: 32324.0
If we subtract 52 from 53, 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.

Advancing to step 7:
10 divided by 13 is 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 32324.0
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.

Let's proceed to step 8:
When dividing 100 by 13, we get 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 32324.07
Deduct 91 from 100 and we're left 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.

Moving on to step 9:
90 divided by 13 is 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 32324.076
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.

Let's proceed to step 10:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 32324.0769
The remainder is 3 after subtracting 117 from 120.
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:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 32324.07692
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.

Moving on to step 12:
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: 32324.076923
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.

On to step 13:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 32324.076923
If we take 0 away from 10, we end up 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.

On to step 14:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 32324.07692307
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 32324.07692307, and the remainder is 9e-09.