We're dividing 177757 by 42 
Our goal is to divide 177757 by 42.

Advancing to step 1:
If we divide 1 by 42, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 42

Going ahead to step 2:
If we divide 17 by 42, we get 0 and a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 17, we get 17.
Grab the next digit (7) from the dividend, add it to 17, then carry on: 177 / 42

Let's proceed to step 3:
If we divide 177 by 42, we get 4 and a remainder of 9.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Subtracting 168 from 177 leaves us with 9.
Include the next digit (7) from the dividend after 9, then repeat: 97 / 42

Step 4:
42 can be fit into 97 2 times, resulting in a remainder of 13.
The number 2 becomes the next digit in our result. 
Result so far: 42.0
Subtracting 84 from 97 leaves us with 13.
Include the next digit (5) from the dividend after 13, then repeat: 135 / 42

On to step 5:
The number 42 fits into 135 3 times, leaving a remainder of 9.
Use 3 as the next digit of our solution. 
Result so far: 423.0
If we take 126 away from 135, we end up with 9.
Append the next digit (7) from the dividend to 9 and continue with: 97 / 42

Advancing to step 6:
If we divide 97 by 42, we get 2 and a remainder of 13.
Record the quotient 2 as the next digit in the result. 
Result so far: 4232.0
Subtracting 84 from 97 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 7:
When dividing 130 by 42, we get 3 with a remainder of 4.
Put 3 as the next digit of the answer. 
Result so far: 4232.3
The remainder is 4 after subtracting 126 from 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
42 can be fit into 40 0 times, resulting in a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 4232.3
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 9:
42 goes into 400 9 times with a remainder of 22.
The next digit of our result is 9. 
Result so far: 4232.309
Deduct 378 from 400 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 10:
42 can be fit into 220 5 times, resulting in a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 4232.3095
Subtracting 210 from 220 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 11:
42 goes into 100 2 times with a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 4232.30952
Subtracting 84 from 100 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 12:
The number 42 fits into 160 3 times, leaving a remainder of 34.
Record the quotient 3 as the next digit in the result. 
Result so far: 4232.309523
Deduct 126 from 160 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Let's proceed to step 13:
42 can be fit into 340 8 times, resulting in a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 4232.3095238
Subtracting 336 from 340 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 14:
40 divided by 42 is 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 4232.3095238
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Our division results in 4232.3095238 with a remaining 4e-08.