6787 ÷ 42 
We want to divide 6787 by 42.

Step 1:
If we divide 6 by 42, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 42

On to step 2:
The number 42 fits into 67 1 times, leaving a remainder of 25.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 25 after subtracting 42 from 67.
Include the next digit (8) from the dividend after 25, then repeat: 258 / 42

Let's proceed to step 3:
42 goes into 258 6 times with a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 16.0
The remainder is 6 after subtracting 252 from 258.
Grab the next digit (7) from the dividend, add it to 6, then carry on: 67 / 42

On to step 4:
67 divided by 42 is 1 with a remainder of 25.
The number 1 becomes the next digit in our result. 
Result so far: 161.0
If we take 42 away from 67, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 5:
The number 42 fits into 250 5 times, leaving a remainder of 40.
The next digit of our result is 5. 
Result so far: 161.5
The remainder is 40 after subtracting 210 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 6:
42 can be fit into 400 9 times, resulting in a remainder of 22.
Write down 9 as next digit of the result. 
Result so far: 161.59
The remainder is 22 after subtracting 378 from 400.
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 7:
When dividing 220 by 42, we get 5 with a remainder of 10.
The next digit of our result is 5. 
Result so far: 161.595
If we take 210 away from 220, we end up 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.

Moving on to step 8:
If we divide 100 by 42, we get 2 and a remainder of 16.
Write down 2 as next digit of the result. 
Result so far: 161.5952
The remainder is 16 after subtracting 84 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 9:
When dividing 160 by 42, we get 3 with a remainder of 34.
The next digit of our result is 3. 
Result so far: 161.59523
Subtracting 126 from 160 leaves us 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.

Going ahead to step 10:
340 divided by 42 is 8 with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 161.595238
The remainder is 4 after subtracting 336 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 11:
42 can be fit into 40 0 times, resulting in a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 161.595238
Subtracting 0 from 40 leaves us 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.

Let's proceed to step 12:
400 divided by 42 is 9 with a remainder of 22.
Use 9 as the next digit of our solution. 
Result so far: 161.59523809
If we take 378 away from 400, we end up 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.

Our division results in 161.59523809 with a remaining 2.2e-08.