511678 ÷ 13 
Let's see how many times 13 fits into 511678.

Let's proceed to step 1:
When dividing 5 by 13, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 13

Step 2:
13 can be fit into 51 3 times, resulting in a remainder of 12.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we take 39 away from 51, we end up with 12.
Take the next digit (1) from the dividend and append it to 12, then repeat: 121 / 13

On to step 3:
13 goes into 121 9 times with a remainder of 4.
The number 9 becomes the next digit in our result. 
Result so far: 39.0
If we subtract 117 from 121, we get 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 13

Moving on to step 4:
When dividing 46 by 13, we get 3 with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 393.0
The remainder is 7 after subtracting 39 from 46.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 13

Step 5:
The number 13 fits into 77 5 times, leaving a remainder of 12.
The next digit of our result is 5. 
Result so far: 3935.0
Deduct 65 from 77 and we're left with 12.
Append the next digit (8) from the dividend to 12 and continue with: 128 / 13

Moving on to step 6:
128 divided by 13 is 9 with a remainder of 11.
Write down 9 as next digit of the result. 
Result so far: 39359.0
The remainder is 11 after subtracting 117 from 128.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 7:
When dividing 110 by 13, we get 8 with a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 39359.8
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.

Let's proceed to step 8:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 39359.84
Subtracting 52 from 60 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 9:
13 goes into 80 6 times with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 39359.846
If we subtract 78 from 80, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 10:
When dividing 20 by 13, we get 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 39359.8461
If we subtract 13 from 20, we 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.

On to step 11:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 39359.84615
Subtract 65 from 70 to 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.

Let's proceed to step 12:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 39359.846153
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 13:
13 goes into 110 8 times with a remainder of 6.
The next digit of our result is 8. 
Result so far: 39359.8461538
If we take 104 away from 110, we end up with 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 14:
When dividing 60 by 13, we get 4 with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 39359.84615384
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.

The final result is 39359.84615384 with a remainder of 8e-09.