85565 divided by 38 
We want to figure out the number of times 85565 can be divided by 38.

Going ahead to step 1:
8 divided by 38 is 0 with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Append the next digit (5) from the dividend to 8 and continue with: 85 / 38

On to step 2:
If we divide 85 by 38, we get 2 and a remainder of 9.
Put 2 as the next digit of the answer. 
Result so far: 2.0
If we subtract 76 from 85, we get 9.
Include the next digit (5) from the dividend after 9, then repeat: 95 / 38

Let's proceed to step 3:
If we divide 95 by 38, we get 2 and a remainder of 19.
Put 2 as the next digit of the answer. 
Result so far: 22.0
The remainder is 19 after subtracting 76 from 95.
Take the next digit (6) from the dividend and append it to 19, then repeat: 196 / 38

Let's proceed to step 4:
38 can be fit into 196 5 times, resulting in a remainder of 6.
The number 5 becomes the next digit in our result. 
Result so far: 225.0
Subtracting 190 from 196 leaves us with 6.
Append the next digit (5) from the dividend to 6 and continue with: 65 / 38

Let's proceed to step 5:
65 divided by 38 is 1 with a remainder of 27.
Put 1 as the next digit of the answer. 
Result so far: 2251.0
If we subtract 38 from 65, we get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 6:
38 goes into 270 7 times with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 2251.7
Deduct 266 from 270 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
38 goes into 40 1 times with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 2251.71
The remainder is 2 after subtracting 38 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
38 goes into 20 0 times with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 2251.71
If we take 0 away from 20, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
38 goes into 200 5 times with a remainder of 10.
The next digit of our result is 5. 
Result so far: 2251.7105
The remainder is 10 after subtracting 190 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 10:
100 divided by 38 is 2 with a remainder of 24.
The number 2 becomes the next digit in our result. 
Result so far: 2251.71052
The remainder is 24 after subtracting 76 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 11:
38 goes into 240 6 times with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 2251.710526
Subtract 228 from 240 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 12:
If we divide 120 by 38, we get 3 and a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 2251.7105263
Deduct 114 from 120 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 13:
The number 38 fits into 60 1 times, leaving a remainder of 22.
Put 1 as the next digit of the answer. 
Result so far: 2251.71052631
Deduct 38 from 60 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

In conclusion, the division gives 2251.71052631 with a balance of 2.2e-08.