We look at the division of 105241 by 78 
We're looking to find how many times 78 goes into 105241.

Advancing to step 1:
78 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 78

Let's proceed to step 2:
78 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Grab the next digit (5) from the dividend, add it to 10, then carry on: 105 / 78

Going ahead to step 3:
78 goes into 105 1 times with a remainder of 27.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 27 after subtracting 78 from 105.
Append the next digit (2) from the dividend to 27 and continue with: 272 / 78

Advancing to step 4:
78 can be fit into 272 3 times, resulting in a remainder of 38.
The next digit of our result is 3. 
Result so far: 13.0
Subtract 234 from 272 to get 38.
Include the next digit (4) from the dividend after 38, then repeat: 384 / 78

On to step 5:
78 goes into 384 4 times with a remainder of 72.
Use 4 as the next digit of our solution. 
Result so far: 134.0
If we take 312 away from 384, we end up with 72.
Bring next digit (1) of the dividend behind the 72 and repeat the process: 721 / 78

Let's proceed to step 6:
When dividing 721 by 78, we get 9 with a remainder of 19.
Use 9 as the next digit of our solution. 
Result so far: 1349.0
The remainder is 19 after subtracting 702 from 721.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

On to step 7:
If we divide 190 by 78, we get 2 and a remainder of 34.
The next digit of our result is 2. 
Result so far: 1349.2
If we take 156 away from 190, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 8:
78 goes into 340 4 times with a remainder of 28.
Use 4 as the next digit of our solution. 
Result so far: 1349.24
Subtract 312 from 340 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 9:
If we divide 280 by 78, we get 3 and a remainder of 46.
Record the quotient 3 as the next digit in the result. 
Result so far: 1349.243
Deduct 234 from 280 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

On to step 10:
78 goes into 460 5 times with a remainder of 70.
The number 5 becomes the next digit in our result. 
Result so far: 1349.2435
If we subtract 390 from 460, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

On to step 11:
700 divided by 78 is 8 with a remainder of 76.
Write down 8 as next digit of the result. 
Result so far: 1349.24358
If we subtract 624 from 700, we get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

On to step 12:
When dividing 760 by 78, we get 9 with a remainder of 58.
Use 9 as the next digit of our solution. 
Result so far: 1349.243589
Deduct 702 from 760 and we're left 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.

Let's proceed to step 13:
78 can be fit into 580 7 times, resulting in a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 1349.2435897
If we subtract 546 from 580, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 14:
78 goes into 340 4 times with a remainder of 28.
Record the quotient 4 as the next digit in the result. 
Result so far: 1349.24358974
If we subtract 312 from 340, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

In conclusion, the division gives 1349.24358974 with a balance of 2.8e-08.