We look at the division of 213619 by 13 
Our goal is to divide 213619 by 13.

On to step 1:
The number 13 fits into 2 0 times, leaving a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 13

Going ahead to step 2:
13 can be fit into 21 1 times, resulting in a remainder of 8.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 13 from 21 and we're left with 8.
Include the next digit (3) from the dividend after 8, then repeat: 83 / 13

Step 3:
13 goes into 83 6 times with a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 16.0
Subtracting 78 from 83 leaves us with 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 13

On to step 4:
13 can be fit into 56 4 times, resulting in a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 164.0
Subtract 52 from 56 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 13

On to step 5:
If we divide 41 by 13, we get 3 and a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 1643.0
Subtracting 39 from 41 leaves us with 2.
Grab the next digit (9) from the dividend, add it to 2, then carry on: 29 / 13

Step 6:
13 goes into 29 2 times with a remainder of 3.
Write down 2 as next digit of the result. 
Result so far: 16432.0
The remainder is 3 after subtracting 26 from 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 7:
30 divided by 13 is 2 with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 16432.2
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.

Moving on to step 8:
13 goes into 40 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 16432.23
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.

Let's proceed to step 9:
13 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 16432.23
Subtracting 0 from 10 leaves us 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.

Step 10:
When dividing 100 by 13, we get 7 with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 16432.2307
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.

Step 11:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 16432.23076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 12:
120 divided by 13 is 9 with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 16432.230769
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.

Moving on to step 13:
30 divided by 13 is 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 16432.2307692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 14:
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: 16432.23076923
If we take 39 away from 40, we end up 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.

The final result is 16432.23076923 with a remainder of 1e-09.