We look at the division of 6340 by 97 
We want to divide 6340 by 97.

Going ahead to step 1:
97 goes into 6 0 times with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 97

Let's proceed to step 2:
97 can be fit into 63 0 times, resulting in a remainder of 63.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 63 to get 63.
Take the next digit (4) from the dividend and append it to 63, then repeat: 634 / 97

Step 3:
97 goes into 634 6 times with a remainder of 52.
Write down 6 as next digit of the result. 
Result so far: 6.0
Deduct 582 from 634 and we're left with 52.
Append the next digit (0) from the dividend to 52 and continue with: 520 / 97

Moving on to step 4:
97 can be fit into 520 5 times, resulting in a remainder of 35.
The number 5 becomes the next digit in our result. 
Result so far: 65.0
Subtract 485 from 520 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 5:
350 divided by 97 is 3 with a remainder of 59.
Use 3 as the next digit of our solution. 
Result so far: 65.3
If we subtract 291 from 350, we get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Going ahead to step 6:
The number 97 fits into 590 6 times, leaving a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 65.36
Subtracting 582 from 590 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.

Advancing to step 7:
80 divided by 97 is 0 with a remainder of 80.
Put 0 as the next digit of the answer. 
Result so far: 65.36
Deduct 0 from 80 and we're left with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Step 8:
If we divide 800 by 97, we get 8 and a remainder of 24.
Write down 8 as next digit of the result. 
Result so far: 65.3608
The remainder is 24 after subtracting 776 from 800.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 9:
97 goes into 240 2 times with a remainder of 46.
Use 2 as the next digit of our solution. 
Result so far: 65.36082
Subtracting 194 from 240 leaves us 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.

Let's proceed to step 10:
97 can be fit into 460 4 times, resulting in a remainder of 72.
Put 4 as the next digit of the answer. 
Result so far: 65.360824
Subtracting 388 from 460 leaves us with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Advancing to step 11:
97 goes into 720 7 times with a remainder of 41.
Record the quotient 7 as the next digit in the result. 
Result so far: 65.3608247
Subtracting 679 from 720 leaves us with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Step 12:
410 divided by 97 is 4 with a remainder of 22.
Write down 4 as next digit of the result. 
Result so far: 65.36082474
If we subtract 388 from 410, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

The quotient of the division is 65.36082474, and the remainder is 2.2e-08.