87591 ÷ 38 
Our goal is to divide 87591 by 38.

Going ahead to step 1:
If we divide 8 by 38, we get 0 and a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Take the next digit (7) from the dividend and append it to 8, then repeat: 87 / 38

Going ahead to step 2:
38 goes into 87 2 times with a remainder of 11.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtracting 76 from 87 leaves us with 11.
Bring next digit (5) of the dividend behind the 11 and repeat the process: 115 / 38

On to step 3:
38 goes into 115 3 times with a remainder of 1.
The next digit of our result is 3. 
Result so far: 23.0
If we subtract 114 from 115, we get 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 38

Let's proceed to step 4:
When dividing 19 by 38, we get 0 with a remainder of 19.
Use 0 as the next digit of our solution. 
Result so far: 230.0
If we take 0 away from 19, we end up with 19.
Append the next digit (1) from the dividend to 19 and continue with: 191 / 38

Step 5:
The number 38 fits into 191 5 times, leaving a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 2305.0
If we subtract 190 from 191, 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.

Going ahead to step 6:
10 divided by 38 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 2305.0
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 7:
If we divide 100 by 38, we get 2 and a remainder of 24.
Put 2 as the next digit of the answer. 
Result so far: 2305.02
Deduct 76 from 100 and we're left 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.

On to step 8:
The number 38 fits into 240 6 times, leaving a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 2305.026
The remainder is 12 after subtracting 228 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 9:
38 can be fit into 120 3 times, resulting in a remainder of 6.
The number 3 becomes the next digit in our result. 
Result so far: 2305.0263
The remainder is 6 after subtracting 114 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 10:
When dividing 60 by 38, we get 1 with a remainder of 22.
Record the quotient 1 as the next digit in the result. 
Result so far: 2305.02631
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.

Moving on to step 11:
220 divided by 38 is 5 with a remainder of 30.
The number 5 becomes the next digit in our result. 
Result so far: 2305.026315
Subtracting 190 from 220 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 12:
The number 38 fits into 300 7 times, leaving a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 2305.0263157
If we take 266 away from 300, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 13:
38 goes into 340 8 times with a remainder of 36.
The next digit of our result is 8. 
Result so far: 2305.02631578
Subtract 304 from 340 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

In conclusion, the division gives 2305.02631578 with a balance of 3.6e-08.