We're dividing 421668 by 42 
We want to figure out the number of times 421668 can be divided by 42.

Let's proceed to step 1:
The number 42 fits into 4 0 times, leaving a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 42

Advancing to step 2:
42 divided by 42 is 1 with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 42 from 42, we get 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 42

Advancing to step 3:
If we divide 1 by 42, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 10.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 42

Let's proceed to step 4:
16 divided by 42 is 0 with a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 100.0
If we subtract 0 from 16, we get 16.
Take the next digit (6) from the dividend and append it to 16, then repeat: 166 / 42

Let's proceed to step 5:
42 can be fit into 166 3 times, resulting in a remainder of 40.
Put 3 as the next digit of the answer. 
Result so far: 1003.0
If we take 126 away from 166, we end up with 40.
Append the next digit (8) from the dividend to 40 and continue with: 408 / 42

On to step 6:
408 divided by 42 is 9 with a remainder of 30.
Write down 9 as next digit of the result. 
Result so far: 10039.0
Deduct 378 from 408 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 7:
42 can be fit into 300 7 times, resulting in a remainder of 6.
Record the quotient 7 as the next digit in the result. 
Result so far: 10039.7
If we subtract 294 from 300, 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.

Let's proceed to step 8:
42 goes into 60 1 times with a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 10039.71
If we subtract 42 from 60, we 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.

Advancing to step 9:
The number 42 fits into 180 4 times, leaving a remainder of 12.
The next digit of our result is 4. 
Result so far: 10039.714
The remainder is 12 after subtracting 168 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 10:
When dividing 120 by 42, we get 2 with a remainder of 36.
The number 2 becomes the next digit in our result. 
Result so far: 10039.7142
Subtracting 84 from 120 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 11:
If we divide 360 by 42, we get 8 and a remainder of 24.
Record the quotient 8 as the next digit in the result. 
Result so far: 10039.71428
Subtracting 336 from 360 leaves us 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.

Moving on to step 12:
If we divide 240 by 42, we get 5 and a remainder of 30.
Put 5 as the next digit of the answer. 
Result so far: 10039.714285
If we take 210 away from 240, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 13:
42 goes into 300 7 times with a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 10039.7142857
Subtract 294 from 300 to 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 14:
When dividing 60 by 42, we get 1 with a remainder of 18.
Use 1 as the next digit of our solution. 
Result so far: 10039.71428571
If we subtract 42 from 60, we 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 outcome is 10039.71428571, with a leftover of 1.8e-08.