105945 ÷ 27 
We're looking to find how many times 27 goes into 105945.

Moving on to step 1:
If we divide 1 by 27, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 27

Going ahead to step 2:
The number 27 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Grab the next digit (5) from the dividend, add it to 10, then carry on: 105 / 27

Advancing to step 3:
When dividing 105 by 27, we get 3 with a remainder of 24.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtract 81 from 105 to get 24.
Grab the next digit (9) from the dividend, add it to 24, then carry on: 249 / 27

Advancing to step 4:
249 divided by 27 is 9 with a remainder of 6.
The next digit of our result is 9. 
Result so far: 39.0
Deduct 243 from 249 and we're left with 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 27

Going ahead to step 5:
27 goes into 64 2 times with a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 392.0
Deduct 54 from 64 and we're left with 10.
Take the next digit (5) from the dividend and append it to 10, then repeat: 105 / 27

Advancing to step 6:
The number 27 fits into 105 3 times, leaving a remainder of 24.
The number 3 becomes the next digit in our result. 
Result so far: 3923.0
Deduct 81 from 105 and we're left 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.

Let's proceed to step 7:
If we divide 240 by 27, we get 8 and a remainder of 24.
The next digit of our result is 8. 
Result so far: 3923.8
If we take 216 away from 240, we end up 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.

Let's proceed to step 8:
27 can be fit into 240 8 times, resulting in a remainder of 24.
Record the quotient 8 as the next digit in the result. 
Result so far: 3923.88
Deduct 216 from 240 and we're left 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.

The final result is 3923.88 with a remainder of 0.024.