We look at the division of 641348 by 13 
We're looking to find how many times 13 goes into 641348.

Let's proceed to step 1:
When dividing 6 by 13, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 13

Let's proceed to step 2:
The number 13 fits into 64 4 times, leaving a remainder of 12.
The next digit of our result is 4. 
Result so far: 4.0
If we subtract 52 from 64, we get 12.
Include the next digit (1) from the dividend after 12, then repeat: 121 / 13

On to step 3:
The number 13 fits into 121 9 times, leaving a remainder of 4.
Write down 9 as next digit of the result. 
Result so far: 49.0
Deduct 117 from 121 and we're left with 4.
Fetch the next digit (3) from the dividend, attach it to 4 and continue: 43 / 13

Moving on to step 4:
43 divided by 13 is 3 with a remainder of 4.
Put 3 as the next digit of the answer. 
Result so far: 493.0
If we subtract 39 from 43, we get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 13

Going ahead to step 5:
If we divide 44 by 13, we get 3 and a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 4933.0
If we take 39 away from 44, we end up with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 13

Step 6:
13 can be fit into 58 4 times, resulting in a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 49334.0
If we subtract 52 from 58, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 7:
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: 49334.4
The remainder is 8 after subtracting 52 from 60.
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 8:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 49334.46
The remainder is 2 after subtracting 78 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 9:
If we divide 20 by 13, we get 1 and a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 49334.461
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.

Going ahead to step 10:
13 goes into 70 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 49334.4615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 11:
50 divided by 13 is 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 49334.46153
Deduct 39 from 50 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 12:
13 goes into 110 8 times with a remainder of 6.
The next digit of our result is 8. 
Result so far: 49334.461538
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.

Moving on to step 13:
13 goes into 60 4 times with a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 49334.4615384
If we take 52 away from 60, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 14:
When dividing 80 by 13, we get 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 49334.46153846
Deduct 78 from 80 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

In conclusion, the division gives 49334.46153846 with a balance of 2e-09.