We're dividing 646309 by 81 
We want to figure out the number of times 646309 can be divided by 81.

Advancing to step 1:
81 can be fit into 6 0 times, resulting in a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 81

Moving on to step 2:
64 divided by 81 is 0 with a remainder of 64.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 64 leaves us with 64.
Bring next digit (6) of the dividend behind the 64 and repeat the process: 646 / 81

Going ahead to step 3:
646 divided by 81 is 7 with a remainder of 79.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Subtract 567 from 646 to get 79.
Grab the next digit (3) from the dividend, add it to 79, then carry on: 793 / 81

Going ahead to step 4:
The number 81 fits into 793 9 times, leaving a remainder of 64.
Record the quotient 9 as the next digit in the result. 
Result so far: 79.0
Subtract 729 from 793 to get 64.
Fetch the next digit (0) from the dividend, attach it to 64 and continue: 640 / 81

Moving on to step 5:
640 divided by 81 is 7 with a remainder of 73.
The number 7 becomes the next digit in our result. 
Result so far: 797.0
If we subtract 567 from 640, we get 73.
Bring next digit (9) of the dividend behind the 73 and repeat the process: 739 / 81

Advancing to step 6:
81 goes into 739 9 times with a remainder of 10.
Write down 9 as next digit of the result. 
Result so far: 7979.0
The remainder is 10 after subtracting 729 from 739.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 7:
If we divide 100 by 81, we get 1 and a remainder of 19.
Put 1 as the next digit of the answer. 
Result so far: 7979.1
Deduct 81 from 100 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Let's proceed to step 8:
81 can be fit into 190 2 times, resulting in a remainder of 28.
The next digit of our result is 2. 
Result so far: 7979.12
Subtract 162 from 190 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 9:
280 divided by 81 is 3 with a remainder of 37.
Use 3 as the next digit of our solution. 
Result so far: 7979.123
Subtracting 243 from 280 leaves us with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Moving on to step 10:
If we divide 370 by 81, we get 4 and a remainder of 46.
Write down 4 as next digit of the result. 
Result so far: 7979.1234
The remainder is 46 after subtracting 324 from 370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Going ahead to step 11:
81 goes into 460 5 times with a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 7979.12345
If we subtract 405 from 460, 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.

On to step 12:
81 goes into 550 6 times with a remainder of 64.
The number 6 becomes the next digit in our result. 
Result so far: 7979.123456
Subtract 486 from 550 to get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Step 13:
640 divided by 81 is 7 with a remainder of 73.
Record the quotient 7 as the next digit in the result. 
Result so far: 7979.1234567
The remainder is 73 after subtracting 567 from 640.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

On to step 14:
81 goes into 730 9 times with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 7979.12345679
Subtract 729 from 730 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The quotient of the division is 7979.12345679, and the remainder is 1e-09.