We're dividing 421097 by 78 
We want to divide 421097 by 78.

Let's proceed to step 1:
78 can be fit into 4 0 times, resulting in a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 78

On to step 2:
78 goes into 42 0 times with a remainder of 42.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 42 to get 42.
Append the next digit (1) from the dividend to 42 and continue with: 421 / 78

Moving on to step 3:
78 can be fit into 421 5 times, resulting in a remainder of 31.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Deduct 390 from 421 and we're left with 31.
Include the next digit (0) from the dividend after 31, then repeat: 310 / 78

Going ahead to step 4:
78 can be fit into 310 3 times, resulting in a remainder of 76.
The number 3 becomes the next digit in our result. 
Result so far: 53.0
Subtract 234 from 310 to get 76.
Take the next digit (9) from the dividend and append it to 76, then repeat: 769 / 78

Step 5:
78 can be fit into 769 9 times, resulting in a remainder of 67.
The number 9 becomes the next digit in our result. 
Result so far: 539.0
Deduct 702 from 769 and we're left with 67.
Grab the next digit (7) from the dividend, add it to 67, then carry on: 677 / 78

Advancing to step 6:
677 divided by 78 is 8 with a remainder of 53.
The next digit of our result is 8. 
Result so far: 5398.0
If we take 624 away from 677, we end up with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Moving on to step 7:
78 goes into 530 6 times with a remainder of 62.
Use 6 as the next digit of our solution. 
Result so far: 5398.6
Subtracting 468 from 530 leaves us with 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 8:
When dividing 620 by 78, we get 7 with a remainder of 74.
Use 7 as the next digit of our solution. 
Result so far: 5398.67
Deduct 546 from 620 and we're left with 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Advancing to step 9:
78 goes into 740 9 times with a remainder of 38.
Use 9 as the next digit of our solution. 
Result so far: 5398.679
Subtract 702 from 740 to get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Going ahead to step 10:
The number 78 fits into 380 4 times, leaving a remainder of 68.
Write down 4 as next digit of the result. 
Result so far: 5398.6794
Deduct 312 from 380 and we're left 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 11:
If we divide 680 by 78, we get 8 and a remainder of 56.
The next digit of our result is 8. 
Result so far: 5398.67948
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.

Advancing to step 12:
78 goes into 560 7 times with a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 5398.679487
Deduct 546 from 560 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 13:
140 divided by 78 is 1 with a remainder of 62.
Record the quotient 1 as the next digit in the result. 
Result so far: 5398.6794871
Subtracting 78 from 140 leaves us with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Going ahead to step 14:
78 can be fit into 620 7 times, resulting in a remainder of 74.
Use 7 as the next digit of our solution. 
Result so far: 5398.67948717
Deduct 546 from 620 and we're left with 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

In conclusion, the division gives 5398.67948717 with a balance of 7.4e-08.