508591 ÷ 97 
We want to figure out the number of times 508591 can be divided by 97.

Advancing to step 1:
97 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 97

On to step 2:
When dividing 50 by 97, we get 0 with a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Append the next digit (8) from the dividend to 50 and continue with: 508 / 97

Step 3:
If we divide 508 by 97, we get 5 and a remainder of 23.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
The remainder is 23 after subtracting 485 from 508.
Fetch the next digit (5) from the dividend, attach it to 23 and continue: 235 / 97

Step 4:
97 goes into 235 2 times with a remainder of 41.
Write down 2 as next digit of the result. 
Result so far: 52.0
If we take 194 away from 235, we end up with 41.
Take the next digit (9) from the dividend and append it to 41, then repeat: 419 / 97

Let's proceed to step 5:
If we divide 419 by 97, we get 4 and a remainder of 31.
The number 4 becomes the next digit in our result. 
Result so far: 524.0
Subtracting 388 from 419 leaves us with 31.
Take the next digit (1) from the dividend and append it to 31, then repeat: 311 / 97

Step 6:
97 can be fit into 311 3 times, resulting in a remainder of 20.
The next digit of our result is 3. 
Result so far: 5243.0
If we subtract 291 from 311, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 7:
The number 97 fits into 200 2 times, leaving a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 5243.2
If we take 194 away from 200, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 8:
97 goes into 60 0 times with a remainder of 60.
Put 0 as the next digit of the answer. 
Result so far: 5243.2
If we subtract 0 from 60, we get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 9:
The number 97 fits into 600 6 times, leaving a remainder of 18.
Put 6 as the next digit of the answer. 
Result so far: 5243.206
If we take 582 away from 600, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 10:
When dividing 180 by 97, we get 1 with a remainder of 83.
Use 1 as the next digit of our solution. 
Result so far: 5243.2061
Deduct 97 from 180 and we're left with 83.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

Going ahead to step 11:
When dividing 830 by 97, we get 8 with a remainder of 54.
Use 8 as the next digit of our solution. 
Result so far: 5243.20618
Subtracting 776 from 830 leaves us with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Moving on to step 12:
When dividing 540 by 97, we get 5 with a remainder of 55.
Write down 5 as next digit of the result. 
Result so far: 5243.206185
If we subtract 485 from 540, we get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 13:
If we divide 550 by 97, we get 5 and a remainder of 65.
The next digit of our result is 5. 
Result so far: 5243.2061855
If we take 485 away from 550, we end up with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The quotient of the division is 5243.2061855, and the remainder is 6.5e-07.