We look at the division of 513608 by 78 
Our goal is to divide 513608 by 78.

Moving on to step 1:
5 divided by 78 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
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:
If we divide 51 by 78, we get 0 and a remainder of 51.
Record the quotient 0 as the next digit in the result. 
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

On to step 3:
78 goes into 513 6 times with a remainder of 45.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 468 from 513, we get 45.
Include the next digit (6) from the dividend after 45, then repeat: 456 / 78

Going ahead to step 4:
78 can be fit into 456 5 times, resulting in a remainder of 66.
Write down 5 as next digit of the result. 
Result so far: 65.0
If we take 390 away from 456, we end up with 66.
Append the next digit (0) from the dividend to 66 and continue with: 660 / 78

Going ahead to step 5:
78 can be fit into 660 8 times, resulting in a remainder of 36.
Record the quotient 8 as the next digit in the result. 
Result so far: 658.0
If we subtract 624 from 660, we get 36.
Grab the next digit (8) from the dividend, add it to 36, then carry on: 368 / 78

Moving on to step 6:
If we divide 368 by 78, we get 4 and a remainder of 56.
Record the quotient 4 as the next digit in the result. 
Result so far: 6584.0
Subtract 312 from 368 to get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Advancing to step 7:
The number 78 fits into 560 7 times, leaving a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 6584.7
If we take 546 away from 560, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 8:
If we divide 140 by 78, we get 1 and a remainder of 62.
Write down 1 as next digit of the result. 
Result so far: 6584.71
If we take 78 away from 140, we end up with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Step 9:
78 goes into 620 7 times with a remainder of 74.
Write down 7 as next digit of the result. 
Result so far: 6584.717
The remainder is 74 after subtracting 546 from 620.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Advancing to step 10:
78 goes into 740 9 times with a remainder of 38.
Put 9 as the next digit of the answer. 
Result so far: 6584.7179
If we take 702 away from 740, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Going ahead to step 11:
The number 78 fits into 380 4 times, leaving a remainder of 68.
Write down 4 as next digit of the result. 
Result so far: 6584.71794
The remainder is 68 after subtracting 312 from 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Let's proceed to step 12:
78 can be fit into 680 8 times, resulting in a remainder of 56.
Write down 8 as next digit of the result. 
Result so far: 6584.717948
Deduct 624 from 680 and we're left with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Let's proceed to step 13:
78 can be fit into 560 7 times, resulting in a remainder of 14.
Use 7 as the next digit of our solution. 
Result so far: 6584.7179487
The remainder is 14 after subtracting 546 from 560.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 14:
140 divided by 78 is 1 with a remainder of 62.
Put 1 as the next digit of the answer. 
Result so far: 6584.71794871
The remainder is 62 after subtracting 78 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

The quotient of the division is 6584.71794871, and the remainder is 6.2e-08.