We're dividing 681606 by 65 
Our goal is to divide 681606 by 65.

Advancing to step 1:
65 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 (8) from the dividend to 6 and continue with: 68 / 65

Advancing to step 2:
68 divided by 65 is 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 65 from 68, we get 3.
Take the next digit (1) from the dividend and append it to 3, then repeat: 31 / 65

Step 3:
The number 65 fits into 31 0 times, leaving a remainder of 31.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we take 0 away from 31, we end up with 31.
Fetch the next digit (6) from the dividend, attach it to 31 and continue: 316 / 65

Let's proceed to step 4:
The number 65 fits into 316 4 times, leaving a remainder of 56.
The number 4 becomes the next digit in our result. 
Result so far: 104.0
Subtracting 260 from 316 leaves us with 56.
Bring next digit (0) of the dividend behind the 56 and repeat the process: 560 / 65

Step 5:
65 can be fit into 560 8 times, resulting in a remainder of 40.
The next digit of our result is 8. 
Result so far: 1048.0
If we take 520 away from 560, we end up with 40.
Take the next digit (6) from the dividend and append it to 40, then repeat: 406 / 65

Moving on to step 6:
65 can be fit into 406 6 times, resulting in a remainder of 16.
Put 6 as the next digit of the answer. 
Result so far: 10486.0
Deduct 390 from 406 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 7:
65 goes into 160 2 times with a remainder of 30.
The number 2 becomes the next digit in our result. 
Result so far: 10486.2
Deduct 130 from 160 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
When dividing 300 by 65, we get 4 with a remainder of 40.
Use 4 as the next digit of our solution. 
Result so far: 10486.24
Deduct 260 from 300 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 9:
If we divide 400 by 65, we get 6 and a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 10486.246
If we subtract 390 from 400, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 10:
100 divided by 65 is 1 with a remainder of 35.
Write down 1 as next digit of the result. 
Result so far: 10486.2461
If we take 65 away from 100, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 11:
350 divided by 65 is 5 with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 10486.24615
If we take 325 away from 350, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 12:
65 goes into 250 3 times with a remainder of 55.
The next digit of our result is 3. 
Result so far: 10486.246153
Subtract 195 from 250 to 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.

Moving on to step 13:
550 divided by 65 is 8 with a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 10486.2461538
Deduct 520 from 550 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 14:
The number 65 fits into 300 4 times, leaving a remainder of 40.
Write down 4 as next digit of the result. 
Result so far: 10486.24615384
If we subtract 260 from 300, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Our division results in 10486.24615384 with a remaining 4e-08.