Let's divide 84078 by 13
We want to divide 84078 by 13.

Advancing to step 1:
13 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Include the next digit (4) from the dividend after 8, then repeat: 84 / 13

Step 2:
If we divide 84 by 13, we get 6 and a remainder of 6.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 78 from 84 and we're left with 6.
Take the next digit (0) from the dividend and append it to 6, then repeat: 60 / 13

On to step 3:
If we divide 60 by 13, we get 4 and a remainder of 8.
The next digit of our result is 4. 
Result so far: 64.0
The remainder is 8 after subtracting 52 from 60.
Fetch the next digit (7) from the dividend, attach it to 8 and continue: 87 / 13

On to step 4:
13 goes into 87 6 times with a remainder of 9.
Record the quotient 6 as the next digit in the result. 
Result so far: 646.0
Subtract 78 from 87 to get 9.
Fetch the next digit (8) from the dividend, attach it to 9 and continue: 98 / 13

Going ahead to step 5:
If we divide 98 by 13, we get 7 and a remainder of 7.
Use 7 as the next digit of our solution. 
Result so far: 6467.0
If we take 91 away from 98, 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.

On to step 6:
If we divide 70 by 13, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 6467.5
Subtracting 65 from 70 leaves us with 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 7:
50 divided by 13 is 3 with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 6467.53
Subtracting 39 from 50 leaves us with 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 8:
When dividing 110 by 13, we get 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 6467.538
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 9:
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: 6467.5384
Subtract 52 from 60 to 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.

Advancing to step 10:
When dividing 80 by 13, we get 6 with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 6467.53846
If we take 78 away from 80, we end up 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.

Advancing to step 11:
13 can be fit into 20 1 times, resulting in a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 6467.538461
Subtracting 13 from 20 leaves us 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 12:
13 goes into 70 5 times with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 6467.5384615
If we take 65 away from 70, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 13:
When dividing 50 by 13, we get 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 6467.53846153
Subtracting 39 from 50 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

The final outcome is 6467.53846153, with a leftover of 1.1e-08.