We look at the division of 17757 by 42 
We're looking to find how many times 42 goes into 17757.

Step 1:
If we divide 1 by 42, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 42

Advancing to step 2:
The number 42 fits into 17 0 times, leaving a remainder of 17.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 17, we get 17.
Fetch the next digit (7) from the dividend, attach it to 17 and continue: 177 / 42

Step 3:
The number 42 fits into 177 4 times, leaving a remainder of 9.
Use 4 as the next digit of our solution. 
Result so far: 4.0
The remainder is 9 after subtracting 168 from 177.
Fetch the next digit (5) from the dividend, attach it to 9 and continue: 95 / 42

On to step 4:
42 can be fit into 95 2 times, resulting in a remainder of 11.
The next digit of our result is 2. 
Result so far: 42.0
If we subtract 84 from 95, we get 11.
Take the next digit (7) from the dividend and append it to 11, then repeat: 117 / 42

On to step 5:
117 divided by 42 is 2 with a remainder of 33.
Put 2 as the next digit of the answer. 
Result so far: 422.0
Subtract 84 from 117 to get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Let's proceed to step 6:
When dividing 330 by 42, we get 7 with a remainder of 36.
Use 7 as the next digit of our solution. 
Result so far: 422.7
Deduct 294 from 330 and we're left 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.

Let's proceed to step 7:
42 can be fit into 360 8 times, resulting in a remainder of 24.
The next digit of our result is 8. 
Result so far: 422.78
Subtract 336 from 360 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 8:
If we divide 240 by 42, we get 5 and a remainder of 30.
The next digit of our result is 5. 
Result so far: 422.785
Subtracting 210 from 240 leaves us 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 9:
300 divided by 42 is 7 with a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 422.7857
Subtracting 294 from 300 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 10:
60 divided by 42 is 1 with a remainder of 18.
Record the quotient 1 as the next digit in the result. 
Result so far: 422.78571
If we take 42 away from 60, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 11:
180 divided by 42 is 4 with a remainder of 12.
Write down 4 as next digit of the result. 
Result so far: 422.785714
Subtracting 168 from 180 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 12:
42 goes into 120 2 times with a remainder of 36.
The next digit of our result is 2. 
Result so far: 422.7857142
If we take 84 away from 120, we end up 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.

Step 13:
If we divide 360 by 42, we get 8 and a remainder of 24.
Put 8 as the next digit of the answer. 
Result so far: 422.78571428
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.

The quotient of the division is 422.78571428, and the remainder is 2.4e-08.