78665 ÷ 71 
Our goal is to divide 78665 by 71.

Moving on to step 1:
The number 71 fits into 7 0 times, leaving a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Take the next digit (8) from the dividend and append it to 7, then repeat: 78 / 71

Going ahead to step 2:
If we divide 78 by 71, we get 1 and a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 71 from 78, we get 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 71

Let's proceed to step 3:
71 can be fit into 76 1 times, resulting in a remainder of 5.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
If we take 71 away from 76, we end up with 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 71

On to step 4:
When dividing 56 by 71, we get 0 with a remainder of 56.
Put 0 as the next digit of the answer. 
Result so far: 110.0
Subtract 0 from 56 to get 56.
Take the next digit (5) from the dividend and append it to 56, then repeat: 565 / 71

Moving on to step 5:
565 divided by 71 is 7 with a remainder of 68.
Record the quotient 7 as the next digit in the result. 
Result so far: 1107.0
Subtracting 497 from 565 leaves us with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Advancing to step 6:
The number 71 fits into 680 9 times, leaving a remainder of 41.
Write down 9 as next digit of the result. 
Result so far: 1107.9
Subtract 639 from 680 to get 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Step 7:
If we divide 410 by 71, we get 5 and a remainder of 55.
Put 5 as the next digit of the answer. 
Result so far: 1107.95
Subtracting 355 from 410 leaves us 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.

On to step 8:
When dividing 550 by 71, we get 7 with a remainder of 53.
Record the quotient 7 as the next digit in the result. 
Result so far: 1107.957
Subtract 497 from 550 to get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Advancing to step 9:
71 goes into 530 7 times with a remainder of 33.
Write down 7 as next digit of the result. 
Result so far: 1107.9577
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.

In conclusion, the division gives 1107.9577 with a balance of 0.00033.