We divide 513541 by 78
We're looking to find how many times 78 goes into 513541.

Advancing to step 1:
78 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 78

Moving on to step 2:
The number 78 fits into 51 0 times, leaving a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Include the next digit (3) from the dividend after 51, then repeat: 513 / 78

Advancing to step 3:
If we divide 513 by 78, we get 6 and a remainder of 45.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we subtract 468 from 513, we get 45.
Bring next digit (5) of the dividend behind the 45 and repeat the process: 455 / 78

Advancing to step 4:
If we divide 455 by 78, we get 5 and a remainder of 65.
Record the quotient 5 as the next digit in the result. 
Result so far: 65.0
Deduct 390 from 455 and we're left with 65.
Take the next digit (4) from the dividend and append it to 65, then repeat: 654 / 78

On to step 5:
When dividing 654 by 78, we get 8 with a remainder of 30.
Put 8 as the next digit of the answer. 
Result so far: 658.0
The remainder is 30 after subtracting 624 from 654.
Take the next digit (1) from the dividend and append it to 30, then repeat: 301 / 78

On to step 6:
When dividing 301 by 78, we get 3 with a remainder of 67.
Write down 3 as next digit of the result. 
Result so far: 6583.0
The remainder is 67 after subtracting 234 from 301.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Going ahead to step 7:
78 can be fit into 670 8 times, resulting in a remainder of 46.
Write down 8 as next digit of the result. 
Result so far: 6583.8
If we subtract 624 from 670, we get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Step 8:
When dividing 460 by 78, we get 5 with a remainder of 70.
Use 5 as the next digit of our solution. 
Result so far: 6583.85
If we subtract 390 from 460, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 9:
78 can be fit into 700 8 times, resulting in a remainder of 76.
Put 8 as the next digit of the answer. 
Result so far: 6583.858
The remainder is 76 after subtracting 624 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Moving on to step 10:
The number 78 fits into 760 9 times, leaving a remainder of 58.
Use 9 as the next digit of our solution. 
Result so far: 6583.8589
The remainder is 58 after subtracting 702 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Moving on to step 11:
78 can be fit into 580 7 times, resulting in a remainder of 34.
Write down 7 as next digit of the result. 
Result so far: 6583.85897
The remainder is 34 after subtracting 546 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 12:
78 can be fit into 340 4 times, resulting in a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 6583.858974
The remainder is 28 after subtracting 312 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 13:
78 goes into 280 3 times with a remainder of 46.
Put 3 as the next digit of the answer. 
Result so far: 6583.8589743
If we take 234 away from 280, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Advancing to step 14:
78 can be fit into 460 5 times, resulting in a remainder of 70.
Write down 5 as next digit of the result. 
Result so far: 6583.85897435
If we take 390 away from 460, we end up with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Our division results in 6583.85897435 with a remaining 7e-08.