6308 ÷ 78 
We want to figure out the number of times 6308 can be divided by 78.

Advancing to step 1:
78 can be fit into 6 0 times, resulting in a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 78

Let's proceed to step 2:
63 divided by 78 is 0 with a remainder of 63.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 63 leaves us with 63.
Grab the next digit (0) from the dividend, add it to 63, then carry on: 630 / 78

Advancing to step 3:
The number 78 fits into 630 8 times, leaving a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
If we take 624 away from 630, we end up with 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 78

Moving on to step 4:
68 divided by 78 is 0 with a remainder of 68.
The number 0 becomes the next digit in our result. 
Result so far: 80.0
If we subtract 0 from 68, we get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Going ahead to step 5:
The number 78 fits into 680 8 times, leaving a remainder of 56.
The number 8 becomes the next digit in our result. 
Result so far: 80.8
Subtracting 624 from 680 leaves us 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.

Moving on to step 6:
78 goes into 560 7 times with a remainder of 14.
The next digit of our result is 7. 
Result so far: 80.87
If we subtract 546 from 560, we get 14.
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 7:
When dividing 140 by 78, we get 1 with a remainder of 62.
Write down 1 as next digit of the result. 
Result so far: 80.871
If we subtract 78 from 140, we get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 8:
When dividing 620 by 78, we get 7 with a remainder of 74.
The number 7 becomes the next digit in our result. 
Result so far: 80.8717
Deduct 546 from 620 and we're left with 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Let's proceed to step 9:
78 goes into 740 9 times with a remainder of 38.
Record the quotient 9 as the next digit in the result. 
Result so far: 80.87179
If we subtract 702 from 740, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

On to step 10:
If we divide 380 by 78, we get 4 and a remainder of 68.
The number 4 becomes the next digit in our result. 
Result so far: 80.871794
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.

On to step 11:
78 goes into 680 8 times with a remainder of 56.
Put 8 as the next digit of the answer. 
Result so far: 80.8717948
Subtract 624 from 680 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.

Going ahead to step 12:
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: 80.87179487
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.

The quotient of the division is 80.87179487, and the remainder is 1.4e-08.