120533 ÷ 13 
Let's see how many times 13 fits into 120533.

Advancing to step 1:
1 divided by 13 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 13

On to step 2:
12 divided by 13 is 0 with a remainder of 12.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 12, we get 12.
Grab the next digit (0) from the dividend, add it to 12, then carry on: 120 / 13

Step 3:
13 can be fit into 120 9 times, resulting in a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
Subtract 117 from 120 to get 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 13

On to step 4:
When dividing 35 by 13, we get 2 with a remainder of 9.
The next digit of our result is 2. 
Result so far: 92.0
The remainder is 9 after subtracting 26 from 35.
Fetch the next digit (3) from the dividend, attach it to 9 and continue: 93 / 13

On to step 5:
When dividing 93 by 13, we get 7 with a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 927.0
Deduct 91 from 93 and we're left with 2.
Append the next digit (3) from the dividend to 2 and continue with: 23 / 13

Step 6:
13 goes into 23 1 times with a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 9271.0
If we subtract 13 from 23, we get 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 7:
13 goes into 100 7 times with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 9271.7
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 8:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The next digit of our result is 6. 
Result so far: 9271.76
Subtract 78 from 90 to 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.

Advancing to step 9:
If we divide 120 by 13, we get 9 and a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 9271.769
Subtract 117 from 120 to 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.

Let's proceed to step 10:
13 can be fit into 30 2 times, resulting in a remainder of 4.
The next digit of our result is 2. 
Result so far: 9271.7692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 11:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 9271.76923
Subtract 39 from 40 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 12:
When dividing 10 by 13, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 9271.76923
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 13:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 9271.7692307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 14:
13 goes into 90 6 times with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 9271.76923076
Deduct 78 from 90 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 9271.76923076 with a remainder of 1.2e-08.