681771 divided by 13 
Our goal is to divide 681771 by 13.

Advancing to step 1:
13 can be fit into 6 0 times, resulting in a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Include the next digit (8) from the dividend after 6, then repeat: 68 / 13

Let's proceed to step 2:
13 goes into 68 5 times with a remainder of 3.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we take 65 away from 68, we end up with 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 13

Let's proceed to step 3:
If we divide 31 by 13, we get 2 and a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 52.0
Subtracting 26 from 31 leaves us with 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 13

Moving on to step 4:
When dividing 57 by 13, we get 4 with a remainder of 5.
Write down 4 as next digit of the result. 
Result so far: 524.0
If we take 52 away from 57, we end up with 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 13

Advancing to step 5:
57 divided by 13 is 4 with a remainder of 5.
Record the quotient 4 as the next digit in the result. 
Result so far: 5244.0
Deduct 52 from 57 and we're left with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 13

Advancing to step 6:
13 can be fit into 51 3 times, resulting in a remainder of 12.
Use 3 as the next digit of our solution. 
Result so far: 52443.0
If we subtract 39 from 51, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 7:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 52443.9
If we subtract 117 from 120, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 8:
13 goes into 30 2 times with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 52443.92
Subtract 26 from 30 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
40 divided by 13 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 52443.923
If we take 39 away from 40, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 10:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 52443.923
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 11:
13 goes into 100 7 times with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 52443.92307
Subtract 91 from 100 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.

Let's proceed to step 12:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 52443.923076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 13:
120 divided by 13 is 9 with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 52443.9230769
Subtract 117 from 120 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 14:
When dividing 30 by 13, we get 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 52443.92307692
Deduct 26 from 30 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Our division results in 52443.92307692 with a remaining 4e-09.