109766 ÷ 60 
We want to figure out the number of times 109766 can be divided by 60.

Step 1:
If we divide 1 by 60, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 60

Going ahead to step 2:
60 can be fit into 10 0 times, resulting in 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.
Include the next digit (9) from the dividend after 10, then repeat: 109 / 60

Going ahead to step 3:
60 goes into 109 1 times with a remainder of 49.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 60 from 109, we get 49.
Take the next digit (7) from the dividend and append it to 49, then repeat: 497 / 60

Advancing to step 4:
When dividing 497 by 60, we get 8 with a remainder of 17.
Record the quotient 8 as the next digit in the result. 
Result so far: 18.0
If we take 480 away from 497, we end up with 17.
Fetch the next digit (6) from the dividend, attach it to 17 and continue: 176 / 60

On to step 5:
If we divide 176 by 60, we get 2 and a remainder of 56.
Write down 2 as next digit of the result. 
Result so far: 182.0
The remainder is 56 after subtracting 120 from 176.
Include the next digit (6) from the dividend after 56, then repeat: 566 / 60

Moving on to step 6:
60 can be fit into 566 9 times, resulting in a remainder of 26.
Record the quotient 9 as the next digit in the result. 
Result so far: 1829.0
Deduct 540 from 566 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 7:
If we divide 260 by 60, we get 4 and a remainder of 20.
The next digit of our result is 4. 
Result so far: 1829.4
Subtracting 240 from 260 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 8:
200 divided by 60 is 3 with a remainder of 20.
The number 3 becomes the next digit in our result. 
Result so far: 1829.43
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 9:
The number 60 fits into 200 3 times, leaving a remainder of 20.
The next digit of our result is 3. 
Result so far: 1829.433
Subtracting 180 from 200 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final outcome is 1829.433, with a leftover of 0.002.