135966 ÷ 48 
We're looking to find how many times 48 goes into 135966.

Going ahead to step 1:
1 divided by 48 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 48

Let's proceed to step 2:
48 can be fit into 13 0 times, resulting in a remainder of 13.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 13, we get 13.
Append the next digit (5) from the dividend to 13 and continue with: 135 / 48

Step 3:
If we divide 135 by 48, we get 2 and a remainder of 39.
The next digit of our result is 2. 
Result so far: 2.0
Subtract 96 from 135 to get 39.
Append the next digit (9) from the dividend to 39 and continue with: 399 / 48

Moving on to step 4:
When dividing 399 by 48, we get 8 with a remainder of 15.
The next digit of our result is 8. 
Result so far: 28.0
Subtract 384 from 399 to get 15.
Grab the next digit (6) from the dividend, add it to 15, then carry on: 156 / 48

On to step 5:
156 divided by 48 is 3 with a remainder of 12.
Write down 3 as next digit of the result. 
Result so far: 283.0
If we take 144 away from 156, we end up with 12.
Fetch the next digit (6) from the dividend, attach it to 12 and continue: 126 / 48

Going ahead to step 6:
126 divided by 48 is 2 with a remainder of 30.
Use 2 as the next digit of our solution. 
Result so far: 2832.0
Deduct 96 from 126 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 7:
If we divide 300 by 48, we get 6 and a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 2832.6
Subtracting 288 from 300 leaves us 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.

Step 8:
48 goes into 120 2 times with a remainder of 24.
Use 2 as the next digit of our solution. 
Result so far: 2832.62
Subtracting 96 from 120 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 9:
48 goes into 240 5 times with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 2832.625
The remainder is 0 after subtracting 240 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 10:
When dividing 0 by 48, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 2832.625
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 11:
48 can be fit into 0 0 times, resulting in a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 2832.625
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Our division results in 2832.625 with a remaining 0.0.