We're dividing 306165 by 88 
We're looking to find how many times 88 goes into 306165.

Step 1:
When dividing 3 by 88, we get 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 88

On to step 2:
If we divide 30 by 88, we get 0 and a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 30, we get 30.
Fetch the next digit (6) from the dividend, attach it to 30 and continue: 306 / 88

Advancing to step 3:
If we divide 306 by 88, we get 3 and a remainder of 42.
Use 3 as the next digit of our solution. 
Result so far: 3.0
If we subtract 264 from 306, we get 42.
Bring next digit (1) of the dividend behind the 42 and repeat the process: 421 / 88

Going ahead to step 4:
If we divide 421 by 88, we get 4 and a remainder of 69.
Write down 4 as next digit of the result. 
Result so far: 34.0
Subtracting 352 from 421 leaves us with 69.
Bring next digit (6) of the dividend behind the 69 and repeat the process: 696 / 88

Going ahead to step 5:
696 divided by 88 is 7 with a remainder of 80.
Record the quotient 7 as the next digit in the result. 
Result so far: 347.0
If we subtract 616 from 696, we get 80.
Take the next digit (5) from the dividend and append it to 80, then repeat: 805 / 88

Step 6:
The number 88 fits into 805 9 times, leaving a remainder of 13.
Put 9 as the next digit of the answer. 
Result so far: 3479.0
If we subtract 792 from 805, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 7:
If we divide 130 by 88, we get 1 and a remainder of 42.
Use 1 as the next digit of our solution. 
Result so far: 3479.1
Subtracting 88 from 130 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 8:
88 goes into 420 4 times with a remainder of 68.
The next digit of our result is 4. 
Result so far: 3479.14
If we subtract 352 from 420, we get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Let's proceed to step 9:
88 goes into 680 7 times with a remainder of 64.
Record the quotient 7 as the next digit in the result. 
Result so far: 3479.147
Subtracting 616 from 680 leaves us with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Going ahead to step 10:
88 can be fit into 640 7 times, resulting in a remainder of 24.
Write down 7 as next digit of the result. 
Result so far: 3479.1477
If we take 616 away from 640, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The quotient of the division is 3479.1477, and the remainder is 0.00024.