663419 ÷ 43 
We want to figure out the number of times 663419 can be divided by 43.

Moving on to step 1:
If we divide 6 by 43, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (6) from the dividend after 6, then repeat: 66 / 43

Moving on to step 2:
The number 43 fits into 66 1 times, leaving a remainder of 23.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 43 from 66, we get 23.
Fetch the next digit (3) from the dividend, attach it to 23 and continue: 233 / 43

Moving on to step 3:
If we divide 233 by 43, we get 5 and a remainder of 18.
The next digit of our result is 5. 
Result so far: 15.0
If we take 215 away from 233, we end up with 18.
Include the next digit (4) from the dividend after 18, then repeat: 184 / 43

Going ahead to step 4:
43 can be fit into 184 4 times, resulting in a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 154.0
Subtracting 172 from 184 leaves us with 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 43

On to step 5:
The number 43 fits into 121 2 times, leaving a remainder of 35.
Put 2 as the next digit of the answer. 
Result so far: 1542.0
Deduct 86 from 121 and we're left with 35.
Bring next digit (9) of the dividend behind the 35 and repeat the process: 359 / 43

Let's proceed to step 6:
When dividing 359 by 43, we get 8 with a remainder of 15.
The next digit of our result is 8. 
Result so far: 15428.0
Subtract 344 from 359 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 7:
If we divide 150 by 43, we get 3 and a remainder of 21.
Record the quotient 3 as the next digit in the result. 
Result so far: 15428.3
If we take 129 away from 150, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 8:
If we divide 210 by 43, we get 4 and a remainder of 38.
Record the quotient 4 as the next digit in the result. 
Result so far: 15428.34
The remainder is 38 after subtracting 172 from 210.
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 9:
If we divide 380 by 43, we get 8 and a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 15428.348
If we subtract 344 from 380, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 10:
When dividing 360 by 43, we get 8 with a remainder of 16.
Record the quotient 8 as the next digit in the result. 
Result so far: 15428.3488
The remainder is 16 after subtracting 344 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final result is 15428.3488 with a remainder of 0.00016.