We're dividing 34166 by 89 
We want to divide 34166 by 89.

Let's proceed to step 1:
If we divide 3 by 89, we get 0 and a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 89

Going ahead to step 2:
If we divide 34 by 89, we get 0 and a remainder of 34.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 34 and we're left with 34.
Fetch the next digit (1) from the dividend, attach it to 34 and continue: 341 / 89

Moving on to step 3:
If we divide 341 by 89, we get 3 and a remainder of 74.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Deduct 267 from 341 and we're left with 74.
Bring next digit (6) of the dividend behind the 74 and repeat the process: 746 / 89

On to step 4:
746 divided by 89 is 8 with a remainder of 34.
The next digit of our result is 8. 
Result so far: 38.0
The remainder is 34 after subtracting 712 from 746.
Fetch the next digit (6) from the dividend, attach it to 34 and continue: 346 / 89

Let's proceed to step 5:
When dividing 346 by 89, we get 3 with a remainder of 79.
Put 3 as the next digit of the answer. 
Result so far: 383.0
Subtracting 267 from 346 leaves us with 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Advancing to step 6:
If we divide 790 by 89, we get 8 and a remainder of 78.
Put 8 as the next digit of the answer. 
Result so far: 383.8
Subtract 712 from 790 to get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Let's proceed to step 7:
89 goes into 780 8 times with a remainder of 68.
The next digit of our result is 8. 
Result so far: 383.88
Deduct 712 from 780 and we're left with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

The final outcome is 383.88, with a leftover of 0.068.