Let's divide 6589 by 97
We want to figure out the number of times 6589 can be divided by 97.

On to step 1:
If we divide 6 by 97, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (5) from the dividend, attach it to 6 and continue: 65 / 97

Advancing to step 2:
The number 97 fits into 65 0 times, leaving a remainder of 65.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 65 and we're left with 65.
Include the next digit (8) from the dividend after 65, then repeat: 658 / 97

Step 3:
If we divide 658 by 97, we get 6 and a remainder of 76.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtract 582 from 658 to get 76.
Include the next digit (9) from the dividend after 76, then repeat: 769 / 97

Advancing to step 4:
97 can be fit into 769 7 times, resulting in a remainder of 90.
Use 7 as the next digit of our solution. 
Result so far: 67.0
If we subtract 679 from 769, we get 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Moving on to step 5:
When dividing 900 by 97, we get 9 with a remainder of 27.
Put 9 as the next digit of the answer. 
Result so far: 67.9
Subtracting 873 from 900 leaves us with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Moving on to step 6:
If we divide 270 by 97, we get 2 and a remainder of 76.
Put 2 as the next digit of the answer. 
Result so far: 67.92
Deduct 194 from 270 and we're left with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Advancing to step 7:
The number 97 fits into 760 7 times, leaving a remainder of 81.
The number 7 becomes the next digit in our result. 
Result so far: 67.927
The remainder is 81 after subtracting 679 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

Going ahead to step 8:
810 divided by 97 is 8 with a remainder of 34.
The next digit of our result is 8. 
Result so far: 67.9278
Deduct 776 from 810 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 9:
When dividing 340 by 97, we get 3 with a remainder of 49.
The number 3 becomes the next digit in our result. 
Result so far: 67.92783
Deduct 291 from 340 and we're left with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Going ahead to step 10:
When dividing 490 by 97, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 67.927835
Deduct 485 from 490 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 11:
When dividing 50 by 97, we get 0 with a remainder of 50.
The next digit of our result is 0. 
Result so far: 67.927835
The remainder is 50 after subtracting 0 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 12:
97 can be fit into 500 5 times, resulting in a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 67.92783505
If we subtract 485 from 500, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

After the division, we end up with 67.92783505 and a remainder of 1.5e-08.