542371 ÷ 13 
Let's see how many times 13 fits into 542371.

Step 1:
The number 13 fits into 5 0 times, leaving a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 13

Step 2:
When dividing 54 by 13, we get 4 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.
Fetch the next digit (2) from the dividend, attach it to 2 and continue: 22 / 13

Going ahead to step 3:
22 divided by 13 is 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 41.0
If we subtract 13 from 22, we get 9.
Bring next digit (3) of the dividend behind the 9 and repeat the process: 93 / 13

Advancing to step 4:
93 divided by 13 is 7 with a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 417.0
Deduct 91 from 93 and we're left with 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 13

Let's proceed to step 5:
27 divided by 13 is 2 with a remainder of 1.
The number 2 becomes the next digit in our result. 
Result so far: 4172.0
Deduct 26 from 27 and we're left with 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 13

Going ahead to step 6:
The number 13 fits into 11 0 times, leaving a remainder of 11.
Put 0 as the next digit of the answer. 
Result so far: 41720.0
If we subtract 0 from 11, 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.

Step 7:
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: 41720.8
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.

Step 8:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 41720.84
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.

Going ahead to step 9:
80 divided by 13 is 6 with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 41720.846
Subtract 78 from 80 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 10:
13 goes into 20 1 times with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 41720.8461
If we take 13 away from 20, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 11:
13 goes into 70 5 times with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 41720.84615
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.

Let's proceed to step 12:
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: 41720.846153
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.

Going ahead to step 13:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 41720.8461538
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.

Step 14:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 41720.84615384
Deduct 52 from 60 and we're left 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.

In conclusion, the division gives 41720.84615384 with a balance of 8e-09.