646413 ÷ 97 
We're looking to find how many times 97 goes into 646413.

On to step 1:
When dividing 6 by 97, we get 0 with a remainder of 6.
The next digit of our result is 0. 
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

Advancing to step 2:
64 divided by 97 is 0 with a remainder of 64.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 64 leaves us with 64.
Append the next digit (6) from the dividend to 64 and continue with: 646 / 97

Moving on to step 3:
When dividing 646 by 97, we get 6 with a remainder of 64.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Deduct 582 from 646 and we're left with 64.
Fetch the next digit (4) from the dividend, attach it to 64 and continue: 644 / 97

On to step 4:
The number 97 fits into 644 6 times, leaving a remainder of 62.
Record the quotient 6 as the next digit in the result. 
Result so far: 66.0
If we subtract 582 from 644, we get 62.
Take the next digit (1) from the dividend and append it to 62, then repeat: 621 / 97

On to step 5:
97 can be fit into 621 6 times, resulting in a remainder of 39.
Write down 6 as next digit of the result. 
Result so far: 666.0
Subtract 582 from 621 to get 39.
Fetch the next digit (3) from the dividend, attach it to 39 and continue: 393 / 97

Step 6:
393 divided by 97 is 4 with a remainder of 5.
The next digit of our result is 4. 
Result so far: 6664.0
Deduct 388 from 393 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.

On to step 7:
When dividing 50 by 97, we get 0 with a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 6664.0
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.

Moving on to step 8:
The number 97 fits into 500 5 times, leaving a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 6664.05
Subtracting 485 from 500 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 9:
The number 97 fits into 150 1 times, leaving a remainder of 53.
Put 1 as the next digit of the answer. 
Result so far: 6664.051
Deduct 97 from 150 and we're left with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Let's proceed to step 10:
97 can be fit into 530 5 times, resulting in a remainder of 45.
Put 5 as the next digit of the answer. 
Result so far: 6664.0515
Subtract 485 from 530 to get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

On to step 11:
When dividing 450 by 97, we get 4 with a remainder of 62.
The next digit of our result is 4. 
Result so far: 6664.05154
If we subtract 388 from 450, 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.

Advancing to step 12:
If we divide 620 by 97, we get 6 and a remainder of 38.
Put 6 as the next digit of the answer. 
Result so far: 6664.051546
Subtracting 582 from 620 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Moving on to step 13:
97 goes into 380 3 times with a remainder of 89.
Use 3 as the next digit of our solution. 
Result so far: 6664.0515463
If we take 291 away from 380, we end up with 89.
Since there are no more digits in the dividend, we add a zero to the remainder making it 890, and continue the process.

Advancing to step 14:
890 divided by 97 is 9 with a remainder of 17.
Use 9 as the next digit of our solution. 
Result so far: 6664.05154639
Deduct 873 from 890 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

The quotient of the division is 6664.05154639, and the remainder is 1.7e-08.