We look at the division of 414429 by 78 
We're looking to find how many times 78 goes into 414429.

Moving on to step 1:
If we divide 4 by 78, we get 0 and a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 78

Let's proceed to step 2:
78 can be fit into 41 0 times, resulting in a remainder of 41.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 41 leaves us with 41.
Append the next digit (4) from the dividend to 41 and continue with: 414 / 78

Going ahead to step 3:
The number 78 fits into 414 5 times, leaving a remainder of 24.
The next digit of our result is 5. 
Result so far: 5.0
Subtract 390 from 414 to get 24.
Take the next digit (4) from the dividend and append it to 24, then repeat: 244 / 78

Going ahead to step 4:
244 divided by 78 is 3 with a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 53.0
If we subtract 234 from 244, we get 10.
Bring next digit (2) of the dividend behind the 10 and repeat the process: 102 / 78

Going ahead to step 5:
When dividing 102 by 78, we get 1 with a remainder of 24.
The next digit of our result is 1. 
Result so far: 531.0
If we subtract 78 from 102, we get 24.
Include the next digit (9) from the dividend after 24, then repeat: 249 / 78

Moving on to step 6:
78 can be fit into 249 3 times, resulting in a remainder of 15.
The number 3 becomes the next digit in our result. 
Result so far: 5313.0
If we take 234 away from 249, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 7:
78 goes into 150 1 times with a remainder of 72.
The next digit of our result is 1. 
Result so far: 5313.1
Deduct 78 from 150 and we're left with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Let's proceed to step 8:
78 can be fit into 720 9 times, resulting in a remainder of 18.
Record the quotient 9 as the next digit in the result. 
Result so far: 5313.19
Subtracting 702 from 720 leaves us 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.

Step 9:
78 can be fit into 180 2 times, resulting in a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 5313.192
If we take 156 away from 180, 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.

On to step 10:
78 goes into 240 3 times with a remainder of 6.
Use 3 as the next digit of our solution. 
Result so far: 5313.1923
If we subtract 234 from 240, we 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.

Advancing to step 11:
When dividing 60 by 78, we get 0 with a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 5313.1923
The remainder is 60 after subtracting 0 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 12:
78 goes into 600 7 times with a remainder of 54.
Use 7 as the next digit of our solution. 
Result so far: 5313.192307
The remainder is 54 after subtracting 546 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

On to step 13:
If we divide 540 by 78, we get 6 and a remainder of 72.
Put 6 as the next digit of the answer. 
Result so far: 5313.1923076
If we subtract 468 from 540, we get 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Advancing to step 14:
When dividing 720 by 78, we get 9 with a remainder of 18.
Put 9 as the next digit of the answer. 
Result so far: 5313.19230769
Subtract 702 from 720 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

The final result is 5313.19230769 with a remainder of 1.8e-08.