We divide 127645 by 3
We want to figure out the number of times 127645 can be divided by 3.

Step 1:
When dividing 1 by 3, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 3

Moving on to step 2:
3 goes into 12 4 times with a remainder of 0.
Write down 4 as next digit of the result. 
Result so far: 4.0
Subtract 12 from 12 to get 0.
Grab the next digit (7) from the dividend, add it to 0, then carry on: 7 / 3

Going ahead to step 3:
The number 3 fits into 7 2 times, leaving a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 42.0
Deduct 6 from 7 and we're left with 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 3

Going ahead to step 4:
16 divided by 3 is 5 with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 425.0
If we subtract 15 from 16, we get 1.
Grab the next digit (4) from the dividend, add it to 1, then carry on: 14 / 3

On to step 5:
If we divide 14 by 3, we get 4 and a remainder of 2.
The next digit of our result is 4. 
Result so far: 4254.0
Subtracting 12 from 14 leaves us with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 3

Let's proceed to step 6:
3 goes into 25 8 times with a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 42548.0
If we take 24 away from 25, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
3 can be fit into 10 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 42548.3
If we subtract 9 from 10, we 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 8:
If we divide 10 by 3, we get 3 and a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 42548.33
If we subtract 9 from 10, we 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.

Our division results in 42548.33 with a remaining 0.001.