106642 ÷ 3 
We're looking to find how many times 3 goes into 106642.

Moving on to step 1:
1 divided by 3 is 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 3

On to step 2:
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: 3.0
Subtracting 9 from 10 leaves us with 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 3

Let's proceed to step 3:
3 can be fit into 16 5 times, resulting in a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 35.0
Subtract 15 from 16 to get 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 3

Moving on to step 4:
The number 3 fits into 16 5 times, leaving a remainder of 1.
Record the quotient 5 as the next digit in the result. 
Result so far: 355.0
The remainder is 1 after subtracting 15 from 16.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 3

Moving on to step 5:
3 goes into 14 4 times with a remainder of 2.
Use 4 as the next digit of our solution. 
Result so far: 3554.0
Deduct 12 from 14 and we're left with 2.
Grab the next digit (2) from the dividend, add it to 2, then carry on: 22 / 3

Let's proceed to step 6:
22 divided by 3 is 7 with a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 35547.0
Deduct 21 from 22 and we're left 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.

Going ahead to step 7:
3 goes into 10 3 times with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 35547.3
Subtract 9 from 10 to 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:
3 goes into 10 3 times with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 35547.33
Subtracting 9 from 10 leaves us 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.

After the division, we end up with 35547.33 and a remainder of 0.001.