405661 ÷ 13 
We want to divide 405661 by 13.

On to step 1:
4 divided by 13 is 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 13

Let's proceed to step 2:
When dividing 40 by 13, we get 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we take 39 away from 40, we end up with 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 13

On to step 3:
If we divide 15 by 13, we get 1 and a remainder of 2.
The next digit of our result is 1. 
Result so far: 31.0
If we subtract 13 from 15, we get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 13

Going ahead to step 4:
13 goes into 26 2 times with a remainder of 0.
Write down 2 as next digit of the result. 
Result so far: 312.0
If we take 26 away from 26, we end up with 0.
Include the next digit (6) from the dividend after 0, then repeat: 6 / 13

Let's proceed to step 5:
13 can be fit into 6 0 times, resulting in a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 3120.0
If we subtract 0 from 6, we get 6.
Grab the next digit (1) from the dividend, add it to 6, then carry on: 61 / 13

Going ahead to step 6:
When dividing 61 by 13, we get 4 with a remainder of 9.
Write down 4 as next digit of the result. 
Result so far: 31204.0
The remainder is 9 after subtracting 52 from 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 7:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 31204.6
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.

Let's proceed to step 8:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 31204.69
Subtracting 117 from 120 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 9:
30 divided by 13 is 2 with a remainder of 4.
The next digit of our result is 2. 
Result so far: 31204.692
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.

Advancing to step 10:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 31204.6923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 11:
The number 13 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 31204.6923
Subtract 0 from 10 to 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.

Advancing to step 12:
The number 13 fits into 100 7 times, leaving a remainder of 9.
The next digit of our result is 7. 
Result so far: 31204.692307
If we take 91 away from 100, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 13:
90 divided by 13 is 6 with a remainder of 12.
The next digit of our result is 6. 
Result so far: 31204.6923076
If we take 78 away from 90, we end up with 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 14:
13 goes into 120 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 31204.69230769
Deduct 117 from 120 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Our division results in 31204.69230769 with a remaining 3e-09.