We're dividing 420605 by 78 
We want to divide 420605 by 78.

Going ahead to step 1:
If we divide 4 by 78, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 78

Moving on to step 2:
When dividing 42 by 78, we get 0 with a remainder of 42.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 42, we end up with 42.
Grab the next digit (0) from the dividend, add it to 42, then carry on: 420 / 78

On to step 3:
If we divide 420 by 78, we get 5 and a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Deduct 390 from 420 and we're left with 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 78

On to step 4:
306 divided by 78 is 3 with a remainder of 72.
Put 3 as the next digit of the answer. 
Result so far: 53.0
Subtracting 234 from 306 leaves us with 72.
Bring next digit (0) of the dividend behind the 72 and repeat the process: 720 / 78

On to step 5:
78 goes into 720 9 times with a remainder of 18.
Record the quotient 9 as the next digit in the result. 
Result so far: 539.0
Subtract 702 from 720 to get 18.
Fetch the next digit (5) from the dividend, attach it to 18 and continue: 185 / 78

Step 6:
185 divided by 78 is 2 with a remainder of 29.
The next digit of our result is 2. 
Result so far: 5392.0
If we subtract 156 from 185, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 7:
290 divided by 78 is 3 with a remainder of 56.
Put 3 as the next digit of the answer. 
Result so far: 5392.3
Subtracting 234 from 290 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Step 8:
If we divide 560 by 78, we get 7 and a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 5392.37
If we subtract 546 from 560, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 9:
140 divided by 78 is 1 with a remainder of 62.
The number 1 becomes the next digit in our result. 
Result so far: 5392.371
Subtract 78 from 140 to get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 10:
620 divided by 78 is 7 with a remainder of 74.
The next digit of our result is 7. 
Result so far: 5392.3717
If we subtract 546 from 620, we get 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Going ahead to step 11:
When dividing 740 by 78, we get 9 with a remainder of 38.
Put 9 as the next digit of the answer. 
Result so far: 5392.37179
If we take 702 away from 740, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Moving on to step 12:
78 goes into 380 4 times with a remainder of 68.
Write down 4 as next digit of the result. 
Result so far: 5392.371794
Subtracting 312 from 380 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.

Let's proceed to step 13:
If we divide 680 by 78, we get 8 and a remainder of 56.
Record the quotient 8 as the next digit in the result. 
Result so far: 5392.3717948
The remainder is 56 after subtracting 624 from 680.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Moving on to step 14:
78 can be fit into 560 7 times, resulting in a remainder of 14.
Record the quotient 7 as the next digit in the result. 
Result so far: 5392.37179487
If we subtract 546 from 560, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

After the division, we end up with 5392.37179487 and a remainder of 1.4e-08.