Let's divide 217674 by 13
We're looking to find how many times 13 goes into 217674.

Going ahead to step 1:
The number 13 fits into 2 0 times, leaving a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 13

On to step 2:
The number 13 fits into 21 1 times, leaving a remainder of 8.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 13 from 21, we get 8.
Append the next digit (7) from the dividend to 8 and continue with: 87 / 13

Let's proceed to step 3:
If we divide 87 by 13, we get 6 and a remainder of 9.
The next digit of our result is 6. 
Result so far: 16.0
If we take 78 away from 87, we end up with 9.
Take the next digit (6) from the dividend and append it to 9, then repeat: 96 / 13

Let's proceed to step 4:
When dividing 96 by 13, we get 7 with a remainder of 5.
Put 7 as the next digit of the answer. 
Result so far: 167.0
Subtracting 91 from 96 leaves us with 5.
Append the next digit (7) from the dividend to 5 and continue with: 57 / 13

Moving on to step 5:
When dividing 57 by 13, we get 4 with a remainder of 5.
The number 4 becomes the next digit in our result. 
Result so far: 1674.0
Deduct 52 from 57 and we're left with 5.
Take the next digit (4) from the dividend and append it to 5, then repeat: 54 / 13

Step 6:
13 goes into 54 4 times with a remainder of 2.
The next digit of our result is 4. 
Result so far: 16744.0
The remainder is 2 after subtracting 52 from 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 7:
When dividing 20 by 13, we get 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 16744.1
If we take 13 away from 20, we end up 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.

Step 8:
13 goes into 70 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 16744.15
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.

Moving on to step 9:
When dividing 50 by 13, we get 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 16744.153
The remainder is 11 after subtracting 39 from 50.
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 10:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 16744.1538
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.

Step 11:
When dividing 60 by 13, we get 4 with a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 16744.15384
If we subtract 52 from 60, we get 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 12:
13 goes into 80 6 times with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 16744.153846
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.

Moving on to step 13:
13 goes into 20 1 times with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 16744.1538461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 14:
70 divided by 13 is 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 16744.15384615
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.

In conclusion, the division gives 16744.15384615 with a balance of 5e-09.