541501 divided by 13 
We're looking to find how many times 13 goes into 541501.

On to step 1:
5 divided by 13 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 13

Let's proceed to step 2:
13 goes into 54 4 times with a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 4.0
If we subtract 52 from 54, we get 2.
Take the next digit (1) from the dividend and append it to 2, then repeat: 21 / 13

Step 3:
If we divide 21 by 13, we get 1 and a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 41.0
Deduct 13 from 21 and we're left with 8.
Take the next digit (5) from the dividend and append it to 8, then repeat: 85 / 13

Advancing to step 4:
13 can be fit into 85 6 times, resulting in a remainder of 7.
Use 6 as the next digit of our solution. 
Result so far: 416.0
Deduct 78 from 85 and we're left with 7.
Fetch the next digit (0) from the dividend, attach it to 7 and continue: 70 / 13

Moving on to step 5:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 4165.0
Subtract 65 from 70 to get 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 13

Moving on to step 6:
13 can be fit into 51 3 times, resulting in a remainder of 12.
The next digit of our result is 3. 
Result so far: 41653.0
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.

Step 7:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 41653.9
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 8:
When dividing 30 by 13, we get 2 with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 41653.92
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to 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: 41653.923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 10:
When dividing 10 by 13, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 41653.923
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 11:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 41653.92307
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.

Moving on to step 12:
If we divide 90 by 13, we get 6 and a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 41653.923076
The remainder is 12 after subtracting 78 from 90.
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 13:
13 goes into 120 9 times with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 41653.9230769
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.

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: 41653.92307692
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

In conclusion, the division gives 41653.92307692 with a balance of 4e-09.