We're dividing 681644 by 13 
Our goal is to divide 681644 by 13.

On to step 1:
13 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 13

Step 2:
If we divide 68 by 13, we get 5 and a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 65 from 68 leaves us with 3.
Append the next digit (1) from the dividend to 3 and continue with: 31 / 13

Advancing to step 3:
If we divide 31 by 13, we get 2 and a remainder of 5.
Write down 2 as next digit of the result. 
Result so far: 52.0
If we subtract 26 from 31, we get 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 13

Moving on to step 4:
13 can be fit into 56 4 times, resulting in a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 524.0
Subtracting 52 from 56 leaves us with 4.
Append the next digit (4) from the dividend to 4 and continue with: 44 / 13

Advancing to step 5:
When dividing 44 by 13, we get 3 with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 5243.0
If we take 39 away from 44, we end up with 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 13

Moving on to step 6:
13 goes into 54 4 times with a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 52434.0
If we subtract 52 from 54, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
20 divided by 13 is 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 52434.1
Subtracting 13 from 20 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 8:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 52434.15
Subtract 65 from 70 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 9:
50 divided by 13 is 3 with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 52434.153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 10:
110 divided by 13 is 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 52434.1538
Subtracting 104 from 110 leaves us 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.

On to step 11:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 52434.15384
If we subtract 52 from 60, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 12:
13 goes into 80 6 times with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 52434.153846
Subtract 78 from 80 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 13:
13 goes into 20 1 times with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 52434.1538461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 14:
13 goes into 70 5 times with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 52434.15384615
If we take 65 away from 70, we end up 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.

In conclusion, the division gives 52434.15384615 with a balance of 5e-09.