219378 ÷ 13 
We're looking to find how many times 13 goes into 219378.

Going ahead to step 1:
13 goes into 2 0 times with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Grab the next digit (1) from the dividend, add it to 2, then carry on: 21 / 13

Let's proceed to step 2:
13 goes into 21 1 times with a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 13 from 21, we get 8.
Bring next digit (9) of the dividend behind the 8 and repeat the process: 89 / 13

Let's proceed to step 3:
The number 13 fits into 89 6 times, leaving a remainder of 11.
The number 6 becomes the next digit in our result. 
Result so far: 16.0
Subtracting 78 from 89 leaves us with 11.
Grab the next digit (3) from the dividend, add it to 11, then carry on: 113 / 13

Moving on to step 4:
13 goes into 113 8 times with a remainder of 9.
The number 8 becomes the next digit in our result. 
Result so far: 168.0
Subtracting 104 from 113 leaves us with 9.
Fetch the next digit (7) from the dividend, attach it to 9 and continue: 97 / 13

Let's proceed to step 5:
13 can be fit into 97 7 times, resulting in a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 1687.0
Subtracting 91 from 97 leaves us with 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 13

On to step 6:
When dividing 68 by 13, we get 5 with a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 16875.0
Deduct 65 from 68 and we're left 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.

Going ahead to step 7:
When dividing 30 by 13, we get 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 16875.2
Deduct 26 from 30 and we're left 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.

Let's proceed to step 8:
When dividing 40 by 13, we get 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 16875.23
Deduct 39 from 40 and we're left 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.

Going ahead to step 9:
10 divided by 13 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 16875.23
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.

Moving on to step 10:
If we divide 100 by 13, we get 7 and a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 16875.2307
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.

Step 11:
90 divided by 13 is 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 16875.23076
Deduct 78 from 90 and we're left 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:
13 goes into 120 9 times with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 16875.230769
Subtracting 117 from 120 leaves us 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.

On to step 13:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 16875.2307692
Subtract 26 from 30 to 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:
When dividing 40 by 13, we get 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 16875.23076923
Subtract 39 from 40 to 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.

In conclusion, the division gives 16875.23076923 with a balance of 1e-09.