We look at the division of 641684 by 77 
Let's see how many times 77 fits into 641684.

Step 1:
6 divided by 77 is 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 77

Advancing to step 2:
77 can be fit into 64 0 times, resulting in a remainder of 64.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 64 and we're left with 64.
Take the next digit (1) from the dividend and append it to 64, then repeat: 641 / 77

On to step 3:
77 can be fit into 641 8 times, resulting in a remainder of 25.
Put 8 as the next digit of the answer. 
Result so far: 8.0
Subtract 616 from 641 to get 25.
Take the next digit (6) from the dividend and append it to 25, then repeat: 256 / 77

Advancing to step 4:
The number 77 fits into 256 3 times, leaving a remainder of 25.
The next digit of our result is 3. 
Result so far: 83.0
If we take 231 away from 256, we end up with 25.
Bring next digit (8) of the dividend behind the 25 and repeat the process: 258 / 77

On to step 5:
If we divide 258 by 77, we get 3 and a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 833.0
Subtract 231 from 258 to get 27.
Grab the next digit (4) from the dividend, add it to 27, then carry on: 274 / 77

Moving on to step 6:
If we divide 274 by 77, we get 3 and a remainder of 43.
The next digit of our result is 3. 
Result so far: 8333.0
Subtract 231 from 274 to 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.

Going ahead to step 7:
77 can be fit into 430 5 times, resulting in a remainder of 45.
Write down 5 as next digit of the result. 
Result so far: 8333.5
If we subtract 385 from 430, we 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.

Advancing to step 8:
When dividing 450 by 77, we get 5 with a remainder of 65.
Write down 5 as next digit of the result. 
Result so far: 8333.55
Deduct 385 from 450 and we're left 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 final outcome is 8333.55, with a leftover of 0.065.