553649 divided by 13 
We're looking to find how many times 13 goes into 553649.

Going ahead to step 1:
13 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 13

Advancing to step 2:
The number 13 fits into 55 4 times, leaving a remainder of 3.
The next digit of our result is 4. 
Result so far: 4.0
Subtract 52 from 55 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 13

Moving on to step 3:
33 divided by 13 is 2 with a remainder of 7.
Record the quotient 2 as the next digit in the result. 
Result so far: 42.0
If we take 26 away from 33, we end up with 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 13

Let's proceed to step 4:
When dividing 76 by 13, we get 5 with a remainder of 11.
The next digit of our result is 5. 
Result so far: 425.0
Subtract 65 from 76 to get 11.
Bring next digit (4) of the dividend behind the 11 and repeat the process: 114 / 13

Advancing to step 5:
The number 13 fits into 114 8 times, leaving a remainder of 10.
Use 8 as the next digit of our solution. 
Result so far: 4258.0
The remainder is 10 after subtracting 104 from 114.
Fetch the next digit (9) from the dividend, attach it to 10 and continue: 109 / 13

On to step 6:
109 divided by 13 is 8 with a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 42588.0
The remainder is 5 after subtracting 104 from 109.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 7:
13 goes into 50 3 times with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 42588.3
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 8:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 42588.38
Subtract 104 from 110 to 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.

Step 9:
If we divide 60 by 13, we get 4 and a remainder of 8.
The next digit of our result is 4. 
Result so far: 42588.384
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.

Step 10:
80 divided by 13 is 6 with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 42588.3846
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.

Step 11:
When dividing 20 by 13, we get 1 with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 42588.38461
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.

Moving on to step 12:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 42588.384615
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.

On to step 13:
When dividing 50 by 13, we get 3 with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 42588.3846153
If we take 39 away from 50, we end up 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.

Moving on to step 14:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 42588.38461538
If we subtract 104 from 110, 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.

In conclusion, the division gives 42588.38461538 with a balance of 6e-09.