7871 ÷ 59 
We want to divide 7871 by 59.

Moving on to step 1:
7 divided by 59 is 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 59

Advancing to step 2:
78 divided by 59 is 1 with a remainder of 19.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 59 from 78, we get 19.
Take the next digit (7) from the dividend and append it to 19, then repeat: 197 / 59

On to step 3:
59 can be fit into 197 3 times, resulting in a remainder of 20.
The next digit of our result is 3. 
Result so far: 13.0
Deduct 177 from 197 and we're left with 20.
Include the next digit (1) from the dividend after 20, then repeat: 201 / 59

Going ahead to step 4:
59 can be fit into 201 3 times, resulting in a remainder of 24.
Write down 3 as next digit of the result. 
Result so far: 133.0
If we take 177 away from 201, 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.

Let's proceed to step 5:
The number 59 fits into 240 4 times, leaving a remainder of 4.
The next digit of our result is 4. 
Result so far: 133.4
The remainder is 4 after subtracting 236 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 6:
40 divided by 59 is 0 with a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 133.4
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 7:
If we divide 400 by 59, we get 6 and a remainder of 46.
The number 6 becomes the next digit in our result. 
Result so far: 133.406
Deduct 354 from 400 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 8:
When dividing 460 by 59, we get 7 with a remainder of 47.
Use 7 as the next digit of our solution. 
Result so far: 133.4067
Subtracting 413 from 460 leaves us with 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Step 9:
The number 59 fits into 470 7 times, leaving a remainder of 57.
The next digit of our result is 7. 
Result so far: 133.40677
If we take 413 away from 470, we end up with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

After the division, we end up with 133.40677 and a remainder of 5.7e-05.