59501 ÷ 71 
We're looking to find how many times 71 goes into 59501.

Going ahead to step 1:
When dividing 5 by 71, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 71

Step 2:
71 can be fit into 59 0 times, resulting in a remainder of 59.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 59 to get 59.
Append the next digit (5) from the dividend to 59 and continue with: 595 / 71

Going ahead to step 3:
The number 71 fits into 595 8 times, leaving a remainder of 27.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Deduct 568 from 595 and we're left with 27.
Take the next digit (0) from the dividend and append it to 27, then repeat: 270 / 71

Advancing to step 4:
71 goes into 270 3 times with a remainder of 57.
The next digit of our result is 3. 
Result so far: 83.0
If we subtract 213 from 270, we get 57.
Bring next digit (1) of the dividend behind the 57 and repeat the process: 571 / 71

Step 5:
571 divided by 71 is 8 with a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 838.0
If we take 568 away from 571, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 6:
The number 71 fits into 30 0 times, leaving a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 838.0
If we take 0 away from 30, we end up 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.

On to step 7:
If we divide 300 by 71, we get 4 and a remainder of 16.
The number 4 becomes the next digit in our result. 
Result so far: 838.04
Subtracting 284 from 300 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 8:
When dividing 160 by 71, we get 2 with a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 838.042
If we take 142 away from 160, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 9:
If we divide 180 by 71, we get 2 and a remainder of 38.
Record the quotient 2 as the next digit in the result. 
Result so far: 838.0422
If we subtract 142 from 180, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The final result is 838.0422 with a remainder of 0.00038.