We divide 78105 by 42
Our goal is to divide 78105 by 42.

Advancing to step 1:
42 goes into 7 0 times with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Take the next digit (8) from the dividend and append it to 7, then repeat: 78 / 42

Moving on to step 2:
78 divided by 42 is 1 with a remainder of 36.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 36 after subtracting 42 from 78.
Include the next digit (1) from the dividend after 36, then repeat: 361 / 42

Going ahead to step 3:
If we divide 361 by 42, we get 8 and a remainder of 25.
The number 8 becomes the next digit in our result. 
Result so far: 18.0
Subtract 336 from 361 to get 25.
Include the next digit (0) from the dividend after 25, then repeat: 250 / 42

Let's proceed to step 4:
If we divide 250 by 42, we get 5 and a remainder of 40.
Put 5 as the next digit of the answer. 
Result so far: 185.0
If we subtract 210 from 250, we get 40.
Grab the next digit (5) from the dividend, add it to 40, then carry on: 405 / 42

On to step 5:
When dividing 405 by 42, we get 9 with a remainder of 27.
Put 9 as the next digit of the answer. 
Result so far: 1859.0
The remainder is 27 after subtracting 378 from 405.
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 6:
If we divide 270 by 42, we get 6 and a remainder of 18.
Record the quotient 6 as the next digit in the result. 
Result so far: 1859.6
The remainder is 18 after subtracting 252 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 7:
180 divided by 42 is 4 with a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 1859.64
If we subtract 168 from 180, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 8:
When dividing 120 by 42, we get 2 with a remainder of 36.
Put 2 as the next digit of the answer. 
Result so far: 1859.642
Subtracting 84 from 120 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 9:
If we divide 360 by 42, we get 8 and a remainder of 24.
Put 8 as the next digit of the answer. 
Result so far: 1859.6428
If we take 336 away from 360, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 10:
If we divide 240 by 42, we get 5 and a remainder of 30.
Put 5 as the next digit of the answer. 
Result so far: 1859.64285
Deduct 210 from 240 and we're left 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.

Let's proceed to step 11:
The number 42 fits into 300 7 times, leaving a remainder of 6.
Use 7 as the next digit of our solution. 
Result so far: 1859.642857
Subtract 294 from 300 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 12:
60 divided by 42 is 1 with a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 1859.6428571
If we take 42 away from 60, 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.

Going ahead to step 13:
180 divided by 42 is 4 with a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 1859.64285714
If we take 168 away from 180, we end up 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.

In conclusion, the division gives 1859.64285714 with a balance of 1.2e-08.