105943 divided by 66 
We're looking to find how many times 66 goes into 105943.

On to step 1:
When dividing 1 by 66, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 66

Let's proceed to step 2:
66 goes into 10 0 times with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 66

Step 3:
66 goes into 105 1 times with a remainder of 39.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 39 after subtracting 66 from 105.
Bring next digit (9) of the dividend behind the 39 and repeat the process: 399 / 66

Advancing to step 4:
When dividing 399 by 66, we get 6 with a remainder of 3.
Record the quotient 6 as the next digit in the result. 
Result so far: 16.0
Deduct 396 from 399 and we're left with 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 66

Advancing to step 5:
66 goes into 34 0 times with a remainder of 34.
Write down 0 as next digit of the result. 
Result so far: 160.0
Subtracting 0 from 34 leaves us with 34.
Include the next digit (3) from the dividend after 34, then repeat: 343 / 66

Let's proceed to step 6:
66 goes into 343 5 times with a remainder of 13.
Write down 5 as next digit of the result. 
Result so far: 1605.0
Subtracting 330 from 343 leaves us 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.

Going ahead to step 7:
66 can be fit into 130 1 times, resulting in a remainder of 64.
Put 1 as the next digit of the answer. 
Result so far: 1605.1
Deduct 66 from 130 and we're left with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Step 8:
When dividing 640 by 66, we get 9 with a remainder of 46.
Write down 9 as next digit of the result. 
Result so far: 1605.19
The remainder is 46 after subtracting 594 from 640.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Advancing to step 9:
When dividing 460 by 66, we get 6 with a remainder of 64.
Record the quotient 6 as the next digit in the result. 
Result so far: 1605.196
The remainder is 64 after subtracting 396 from 460.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

On to step 10:
640 divided by 66 is 9 with a remainder of 46.
Put 9 as the next digit of the answer. 
Result so far: 1605.1969
Deduct 594 from 640 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

On to step 11:
66 goes into 460 6 times with a remainder of 64.
Write down 6 as next digit of the result. 
Result so far: 1605.19696
Subtract 396 from 460 to get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 12:
66 can be fit into 640 9 times, resulting in a remainder of 46.
Put 9 as the next digit of the answer. 
Result so far: 1605.196969
If we take 594 away from 640, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 13:
66 goes into 460 6 times with a remainder of 64.
Use 6 as the next digit of our solution. 
Result so far: 1605.1969696
If we take 396 away from 460, we end up with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 14:
When dividing 640 by 66, we get 9 with a remainder of 46.
The next digit of our result is 9. 
Result so far: 1605.19696969
Subtracting 594 from 640 leaves us with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

The final outcome is 1605.19696969, with a leftover of 4.6e-08.