We're dividing 13117 by 24 
We want to divide 13117 by 24.

Moving on to step 1:
The number 24 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 24

On to step 2:
24 goes into 13 0 times with a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 13, we get 13.
Bring next digit (1) of the dividend behind the 13 and repeat the process: 131 / 24

Moving on to step 3:
If we divide 131 by 24, we get 5 and a remainder of 11.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
The remainder is 11 after subtracting 120 from 131.
Take the next digit (1) from the dividend and append it to 11, then repeat: 111 / 24

Let's proceed to step 4:
When dividing 111 by 24, we get 4 with a remainder of 15.
Put 4 as the next digit of the answer. 
Result so far: 54.0
Deduct 96 from 111 and we're left with 15.
Grab the next digit (7) from the dividend, add it to 15, then carry on: 157 / 24

On to step 5:
If we divide 157 by 24, we get 6 and a remainder of 13.
Use 6 as the next digit of our solution. 
Result so far: 546.0
Deduct 144 from 157 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 6:
When dividing 130 by 24, we get 5 with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 546.5
Deduct 120 from 130 and we're left 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.

Moving on to step 7:
100 divided by 24 is 4 with a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 546.54
If we take 96 away from 100, we end up with 4.
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 8:
When dividing 40 by 24, we get 1 with a remainder of 16.
Record the quotient 1 as the next digit in the result. 
Result so far: 546.541
Subtracting 24 from 40 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 9:
If we divide 160 by 24, we get 6 and a remainder of 16.
Use 6 as the next digit of our solution. 
Result so far: 546.5416
If we subtract 144 from 160, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 10:
When dividing 160 by 24, we get 6 with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 546.54166
Subtracting 144 from 160 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

In conclusion, the division gives 546.54166 with a balance of 1.6e-05.