43661 ÷ 78 
We want to divide 43661 by 78.

Going ahead to step 1:
The number 78 fits into 4 0 times, leaving a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 78

Advancing to step 2:
78 can be fit into 43 0 times, resulting in a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 43, we get 43.
Include the next digit (6) from the dividend after 43, then repeat: 436 / 78

Step 3:
The number 78 fits into 436 5 times, leaving a remainder of 46.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we subtract 390 from 436, we get 46.
Append the next digit (6) from the dividend to 46 and continue with: 466 / 78

On to step 4:
78 can be fit into 466 5 times, resulting in a remainder of 76.
Use 5 as the next digit of our solution. 
Result so far: 55.0
Deduct 390 from 466 and we're left with 76.
Fetch the next digit (1) from the dividend, attach it to 76 and continue: 761 / 78

Going ahead to step 5:
When dividing 761 by 78, we get 9 with a remainder of 59.
Put 9 as the next digit of the answer. 
Result so far: 559.0
If we subtract 702 from 761, we get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Moving on to step 6:
78 goes into 590 7 times with a remainder of 44.
The next digit of our result is 7. 
Result so far: 559.7
Subtract 546 from 590 to get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 7:
78 can be fit into 440 5 times, resulting in a remainder of 50.
Put 5 as the next digit of the answer. 
Result so far: 559.75
Subtracting 390 from 440 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

On to step 8:
If we divide 500 by 78, we get 6 and a remainder of 32.
Record the quotient 6 as the next digit in the result. 
Result so far: 559.756
If we subtract 468 from 500, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 9:
78 can be fit into 320 4 times, resulting in a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 559.7564
If we subtract 312 from 320, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 10:
The number 78 fits into 80 1 times, leaving a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 559.75641
Deduct 78 from 80 and we're left 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.

Step 11:
78 can be fit into 20 0 times, resulting in a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 559.75641
The remainder is 20 after subtracting 0 from 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 12:
The number 78 fits into 200 2 times, leaving a remainder of 44.
The number 2 becomes the next digit in our result. 
Result so far: 559.7564102
If we subtract 156 from 200, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Going ahead to step 13:
The number 78 fits into 440 5 times, leaving a remainder of 50.
Use 5 as the next digit of our solution. 
Result so far: 559.75641025
Deduct 390 from 440 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

In conclusion, the division gives 559.75641025 with a balance of 5e-08.