We're dividing 641475 by 97 
Our goal is to divide 641475 by 97.

Moving on to step 1:
6 divided by 97 is 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 97

On to step 2:
64 divided by 97 is 0 with a remainder of 64.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 64 and we're left with 64.
Bring next digit (1) of the dividend behind the 64 and repeat the process: 641 / 97

Advancing to step 3:
97 goes into 641 6 times with a remainder of 59.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtract 582 from 641 to get 59.
Fetch the next digit (4) from the dividend, attach it to 59 and continue: 594 / 97

Going ahead to step 4:
If we divide 594 by 97, we get 6 and a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 66.0
If we take 582 away from 594, we end up with 12.
Take the next digit (7) from the dividend and append it to 12, then repeat: 127 / 97

Going ahead to step 5:
The number 97 fits into 127 1 times, leaving a remainder of 30.
Put 1 as the next digit of the answer. 
Result so far: 661.0
If we take 97 away from 127, we end up with 30.
Bring next digit (5) of the dividend behind the 30 and repeat the process: 305 / 97

Step 6:
If we divide 305 by 97, we get 3 and a remainder of 14.
The next digit of our result is 3. 
Result so far: 6613.0
Subtracting 291 from 305 leaves us 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.

Going ahead to step 7:
97 can be fit into 140 1 times, resulting in a remainder of 43.
Use 1 as the next digit of our solution. 
Result so far: 6613.1
If we subtract 97 from 140, we get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 8:
97 can be fit into 430 4 times, resulting in a remainder of 42.
The next digit of our result is 4. 
Result so far: 6613.14
The remainder is 42 after subtracting 388 from 430.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 9:
97 can be fit into 420 4 times, resulting in a remainder of 32.
Record the quotient 4 as the next digit in the result. 
Result so far: 6613.144
If we subtract 388 from 420, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The quotient of the division is 6613.144, and the remainder is 0.0032.