We divide 565661 by 13
We're looking to find how many times 13 goes into 565661.

Let's proceed to step 1:
When dividing 5 by 13, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 13

On to step 2:
13 can be fit into 56 4 times, resulting in a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 4.0
Subtract 52 from 56 to get 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 13

Going ahead to step 3:
13 goes into 45 3 times with a remainder of 6.
The number 3 becomes the next digit in our result. 
Result so far: 43.0
If we subtract 39 from 45, we get 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 13

On to step 4:
66 divided by 13 is 5 with a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 435.0
The remainder is 1 after subtracting 65 from 66.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 13

Advancing to step 5:
16 divided by 13 is 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 4351.0
Subtract 13 from 16 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 13

On to step 6:
13 can be fit into 31 2 times, resulting in a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 43512.0
Subtract 26 from 31 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.

Going ahead to step 7:
If we divide 50 by 13, we get 3 and a remainder of 11.
The next digit of our result is 3. 
Result so far: 43512.3
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.

Going ahead to step 8:
When dividing 110 by 13, we get 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 43512.38
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 9:
13 goes into 60 4 times with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 43512.384
Subtract 52 from 60 to 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.

Advancing to step 10:
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: 43512.3846
If we take 78 away from 80, we end up 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.

On to step 11:
20 divided by 13 is 1 with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 43512.38461
The remainder is 7 after subtracting 13 from 20.
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 12:
When dividing 70 by 13, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 43512.384615
If we subtract 65 from 70, we 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.

Advancing to step 13:
If we divide 50 by 13, we get 3 and a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 43512.3846153
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 14:
110 divided by 13 is 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 43512.38461538
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

In conclusion, the division gives 43512.38461538 with a balance of 6e-09.