We look at the division of 542645 by 42 
We're looking to find how many times 42 goes into 542645.

Let's proceed to step 1:
If we divide 5 by 42, we get 0 and a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (4) from the dividend after 5, then repeat: 54 / 42

Advancing to step 2:
The number 42 fits into 54 1 times, leaving a remainder of 12.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 42 from 54, we get 12.
Append the next digit (2) from the dividend to 12 and continue with: 122 / 42

Going ahead to step 3:
When dividing 122 by 42, we get 2 with a remainder of 38.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Subtract 84 from 122 to get 38.
Bring next digit (6) of the dividend behind the 38 and repeat the process: 386 / 42

Let's proceed to step 4:
386 divided by 42 is 9 with a remainder of 8.
Write down 9 as next digit of the result. 
Result so far: 129.0
If we take 378 away from 386, we end up with 8.
Grab the next digit (4) from the dividend, add it to 8, then carry on: 84 / 42

Advancing to step 5:
When dividing 84 by 42, we get 2 with a remainder of 0.
Write down 2 as next digit of the result. 
Result so far: 1292.0
If we subtract 84 from 84, we get 0.
Append the next digit (5) from the dividend to 0 and continue with: 5 / 42

Going ahead to step 6:
If we divide 5 by 42, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 12920.0
If we subtract 0 from 5, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 7:
50 divided by 42 is 1 with a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 12920.1
Subtract 42 from 50 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 8:
The number 42 fits into 80 1 times, leaving a remainder of 38.
Record the quotient 1 as the next digit in the result. 
Result so far: 12920.11
Deduct 42 from 80 and we're left 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.

After the division, we end up with 12920.11 and a remainder of 0.038.