We're dividing 681264 by 51 
We want to divide 681264 by 51.

On to step 1:
If we divide 6 by 51, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 51

Going ahead to step 2:
68 divided by 51 is 1 with a remainder of 17.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 51 from 68, we get 17.
Append the next digit (1) from the dividend to 17 and continue with: 171 / 51

Let's proceed to step 3:
The number 51 fits into 171 3 times, leaving a remainder of 18.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we subtract 153 from 171, we get 18.
Grab the next digit (2) from the dividend, add it to 18, then carry on: 182 / 51

Going ahead to step 4:
51 goes into 182 3 times with a remainder of 29.
Record the quotient 3 as the next digit in the result. 
Result so far: 133.0
Deduct 153 from 182 and we're left with 29.
Grab the next digit (6) from the dividend, add it to 29, then carry on: 296 / 51

Step 5:
51 goes into 296 5 times with a remainder of 41.
Put 5 as the next digit of the answer. 
Result so far: 1335.0
Subtracting 255 from 296 leaves us with 41.
Include the next digit (4) from the dividend after 41, then repeat: 414 / 51

Going ahead to step 6:
When dividing 414 by 51, we get 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 13358.0
Deduct 408 from 414 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 7:
51 can be fit into 60 1 times, resulting in a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 13358.1
Subtract 51 from 60 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 8:
51 goes into 90 1 times with a remainder of 39.
The number 1 becomes the next digit in our result. 
Result so far: 13358.11
Deduct 51 from 90 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

The final result is 13358.11 with a remainder of 0.039.