165967 ÷ 3 
Our goal is to divide 165967 by 3.

Going ahead to 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
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 3

On to step 2:
3 can be fit into 16 5 times, resulting in a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 15 away from 16, we end up with 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

Moving on to step 3:
15 divided by 3 is 5 with a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 55.0
Deduct 15 from 15 and we're left with 0.
Grab the next digit (9) from the dividend, add it to 0, then carry on: 9 / 3

Advancing to step 4:
If we divide 9 by 3, we get 3 and a remainder of 0.
Use 3 as the next digit of our solution. 
Result so far: 553.0
Subtracting 9 from 9 leaves us with 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 3

Going ahead to step 5:
If we divide 6 by 3, we get 2 and a remainder of 0.
The next digit of our result is 2. 
Result so far: 5532.0
Subtract 6 from 6 to get 0.
Include the next digit (7) from the dividend after 0, then repeat: 7 / 3

Moving on to 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: 55322.0
Deduct 6 from 7 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.

Advancing to step 7:
10 divided by 3 is 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 55322.3
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.

Moving on to step 8:
3 goes into 10 3 times with a remainder of 1.
The next digit of our result is 3. 
Result so far: 55322.33
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.

In conclusion, the division gives 55322.33 with a balance of 0.001.