101159 ÷ 71 
We're looking to find how many times 71 goes into 101159.

On to step 1:
When dividing 1 by 71, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 71

Step 2:
10 divided by 71 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 71

Let's proceed to step 3:
When dividing 101 by 71, we get 1 with a remainder of 30.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 71 from 101 and we're left with 30.
Bring next digit (1) of the dividend behind the 30 and repeat the process: 301 / 71

Let's proceed to step 4:
71 goes into 301 4 times with a remainder of 17.
The next digit of our result is 4. 
Result so far: 14.0
Deduct 284 from 301 and we're left with 17.
Take the next digit (5) from the dividend and append it to 17, then repeat: 175 / 71

Going ahead to step 5:
71 goes into 175 2 times with a remainder of 33.
Put 2 as the next digit of the answer. 
Result so far: 142.0
If we subtract 142 from 175, we get 33.
Grab the next digit (9) from the dividend, add it to 33, then carry on: 339 / 71

Advancing to step 6:
339 divided by 71 is 4 with a remainder of 55.
Record the quotient 4 as the next digit in the result. 
Result so far: 1424.0
If we take 284 away from 339, we end up with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Advancing to step 7:
When dividing 550 by 71, we get 7 with a remainder of 53.
Put 7 as the next digit of the answer. 
Result so far: 1424.7
Subtracting 497 from 550 leaves us with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Moving on to step 8:
When dividing 530 by 71, we get 7 with a remainder of 33.
Put 7 as the next digit of the answer. 
Result so far: 1424.77
If we take 497 away from 530, we end up with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

The final result is 1424.77 with a remainder of 0.033.