1660 ÷ 71 
We're looking to find how many times 71 goes into 1660.

Advancing to step 1:
71 can be fit into 1 0 times, resulting in a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 71

Moving on to step 2:
When dividing 16 by 71, we get 0 with a remainder of 16.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 16 to get 16.
Grab the next digit (6) from the dividend, add it to 16, then carry on: 166 / 71

Going ahead to step 3:
166 divided by 71 is 2 with a remainder of 24.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Deduct 142 from 166 and we're left with 24.
Grab the next digit (0) from the dividend, add it to 24, then carry on: 240 / 71

Step 4:
71 goes into 240 3 times with a remainder of 27.
Use 3 as the next digit of our solution. 
Result so far: 23.0
Deduct 213 from 240 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 5:
71 can be fit into 270 3 times, resulting in a remainder of 57.
Record the quotient 3 as the next digit in the result. 
Result so far: 23.3
If we take 213 away from 270, 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.

On to step 6:
71 goes into 570 8 times with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 23.38
If we take 568 away from 570, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 7:
When dividing 20 by 71, we get 0 with a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 23.38
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.

Let's proceed to step 8:
The number 71 fits into 200 2 times, leaving a remainder of 58.
The number 2 becomes the next digit in our result. 
Result so far: 23.3802
Subtracting 142 from 200 leaves us with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Going ahead to step 9:
When dividing 580 by 71, we get 8 with a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 23.38028
Deduct 568 from 580 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 10:
The number 71 fits into 120 1 times, leaving a remainder of 49.
The next digit of our result is 1. 
Result so far: 23.380281
The remainder is 49 after subtracting 71 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Step 11:
When dividing 490 by 71, we get 6 with a remainder of 64.
The number 6 becomes the next digit in our result. 
Result so far: 23.3802816
If we subtract 426 from 490, we get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 12:
71 goes into 640 9 times with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 23.38028169
Subtracting 639 from 640 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 23.38028169 with a balance of 1e-09.