We're dividing 513609 by 78 
Let's see how many times 78 fits into 513609.

Step 1:
If we divide 5 by 78, we get 0 and a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 78

Step 2:
If we divide 51 by 78, we get 0 and a remainder of 51.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 51 leaves us with 51.
Bring next digit (3) of the dividend behind the 51 and repeat the process: 513 / 78

Let's proceed to step 3:
When dividing 513 by 78, we get 6 with a remainder of 45.
The next digit of our result is 6. 
Result so far: 6.0
Deduct 468 from 513 and we're left with 45.
Grab the next digit (6) from the dividend, add it to 45, then carry on: 456 / 78

Advancing to step 4:
If we divide 456 by 78, we get 5 and a remainder of 66.
The next digit of our result is 5. 
Result so far: 65.0
If we subtract 390 from 456, we get 66.
Include the next digit (0) from the dividend after 66, then repeat: 660 / 78

Going ahead to step 5:
If we divide 660 by 78, we get 8 and a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 658.0
If we take 624 away from 660, we end up with 36.
Include the next digit (9) from the dividend after 36, then repeat: 369 / 78

Moving on to step 6:
If we divide 369 by 78, we get 4 and a remainder of 57.
Put 4 as the next digit of the answer. 
Result so far: 6584.0
The remainder is 57 after subtracting 312 from 369.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

On to step 7:
570 divided by 78 is 7 with a remainder of 24.
The next digit of our result is 7. 
Result so far: 6584.7
If we take 546 away from 570, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 8:
If we divide 240 by 78, we get 3 and a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 6584.73
If we take 234 away from 240, 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.

Moving on to step 9:
78 goes into 60 0 times with a remainder of 60.
Write down 0 as next digit of the result. 
Result so far: 6584.73
Subtract 0 from 60 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 10:
If we divide 600 by 78, we get 7 and a remainder of 54.
Use 7 as the next digit of our solution. 
Result so far: 6584.7307
The remainder is 54 after subtracting 546 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Advancing to step 11:
If we divide 540 by 78, we get 6 and a remainder of 72.
Use 6 as the next digit of our solution. 
Result so far: 6584.73076
Subtract 468 from 540 to get 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Let's proceed to step 12:
When dividing 720 by 78, we get 9 with a remainder of 18.
Record the quotient 9 as the next digit in the result. 
Result so far: 6584.730769
If we subtract 702 from 720, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 13:
78 can be fit into 180 2 times, resulting in a remainder of 24.
Use 2 as the next digit of our solution. 
Result so far: 6584.7307692
Subtracting 156 from 180 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 14:
78 goes into 240 3 times with a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 6584.73076923
Deduct 234 from 240 and we're left 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.

In conclusion, the division gives 6584.73076923 with a balance of 6e-09.