643142 ÷ 42 
We're looking to find how many times 42 goes into 643142.

Step 1:
42 can be fit into 6 0 times, resulting in a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 42

Going ahead to step 2:
If we divide 64 by 42, we get 1 and a remainder of 22.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 42 from 64 and we're left with 22.
Include the next digit (3) from the dividend after 22, then repeat: 223 / 42

Step 3:
If we divide 223 by 42, we get 5 and a remainder of 13.
Write down 5 as next digit of the result. 
Result so far: 15.0
If we subtract 210 from 223, we get 13.
Take the next digit (1) from the dividend and append it to 13, then repeat: 131 / 42

Going ahead to step 4:
The number 42 fits into 131 3 times, leaving a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 153.0
Subtracting 126 from 131 leaves us with 5.
Include the next digit (4) from the dividend after 5, then repeat: 54 / 42

On to step 5:
42 goes into 54 1 times with a remainder of 12.
Use 1 as the next digit of our solution. 
Result so far: 1531.0
The remainder is 12 after subtracting 42 from 54.
Append the next digit (2) from the dividend to 12 and continue with: 122 / 42

Let's proceed to step 6:
If we divide 122 by 42, we get 2 and a remainder of 38.
Use 2 as the next digit of our solution. 
Result so far: 15312.0
If we take 84 away from 122, 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 7:
The number 42 fits into 380 9 times, leaving a remainder of 2.
The next digit of our result is 9. 
Result so far: 15312.9
Subtracting 378 from 380 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
20 divided by 42 is 0 with a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 15312.9
If we take 0 away from 20, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 9:
200 divided by 42 is 4 with a remainder of 32.
Write down 4 as next digit of the result. 
Result so far: 15312.904
Subtract 168 from 200 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 10:
When dividing 320 by 42, we get 7 with a remainder of 26.
Use 7 as the next digit of our solution. 
Result so far: 15312.9047
The remainder is 26 after subtracting 294 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Going ahead to step 11:
If we divide 260 by 42, we get 6 and a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 15312.90476
If we take 252 away from 260, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 12:
42 can be fit into 80 1 times, resulting in a remainder of 38.
Record the quotient 1 as the next digit in the result. 
Result so far: 15312.904761
If we take 42 away from 80, 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.

Let's proceed to step 13:
42 can be fit into 380 9 times, resulting in a remainder of 2.
Write down 9 as next digit of the result. 
Result so far: 15312.9047619
If we subtract 378 from 380, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 14:
When dividing 20 by 42, we get 0 with a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 15312.9047619
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The quotient of the division is 15312.9047619, and the remainder is 2e-08.