Let's divide 106567 by 3
Our goal is to divide 106567 by 3.

On to step 1:
3 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 3

Going ahead to step 2:
The number 3 fits into 10 3 times, leaving a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 9 from 10, we get 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 3

Moving on to step 3:
If we divide 16 by 3, we get 5 and a remainder of 1.
The next digit of our result is 5. 
Result so far: 35.0
Deduct 15 from 16 and we're left with 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

Let's proceed to step 4:
When dividing 15 by 3, we get 5 with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 355.0
If we take 15 away from 15, we end up with 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 3

Advancing to step 5:
3 can be fit into 6 2 times, resulting in a remainder of 0.
Write down 2 as next digit of the result. 
Result so far: 3552.0
Deduct 6 from 6 and we're left with 0.
Take the next digit (7) from the dividend and append it to 0, then repeat: 7 / 3

Step 6:
3 can be fit into 7 2 times, resulting in a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 35522.0
The remainder is 1 after subtracting 6 from 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
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: 35522.3
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.

Moving on to step 8:
When dividing 10 by 3, we get 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 35522.33
If we take 9 away from 10, 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.

The final outcome is 35522.33, with a leftover of 0.001.