We divide 8677 by 42
We want to figure out the number of times 8677 can be divided by 42.

Moving on to step 1:
8 divided by 42 is 0 with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Grab the next digit (6) from the dividend, add it to 8, then carry on: 86 / 42

Step 2:
86 divided by 42 is 2 with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we subtract 84 from 86, we get 2.
Include the next digit (7) from the dividend after 2, then repeat: 27 / 42

Advancing to step 3:
When dividing 27 by 42, we get 0 with a remainder of 27.
Record the quotient 0 as the next digit in the result. 
Result so far: 20.0
Subtract 0 from 27 to get 27.
Grab the next digit (7) from the dividend, add it to 27, then carry on: 277 / 42

Going ahead to step 4:
If we divide 277 by 42, we get 6 and a remainder of 25.
Put 6 as the next digit of the answer. 
Result so far: 206.0
If we take 252 away from 277, 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.

On to step 5:
42 can be fit into 250 5 times, resulting in a remainder of 40.
Use 5 as the next digit of our solution. 
Result so far: 206.5
Subtracting 210 from 250 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.

Step 6:
If we divide 400 by 42, we get 9 and a remainder of 22.
The number 9 becomes the next digit in our result. 
Result so far: 206.59
Subtract 378 from 400 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 7:
42 can be fit into 220 5 times, resulting in a remainder of 10.
The next digit of our result is 5. 
Result so far: 206.595
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.

Step 8:
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: 206.5952
If we subtract 84 from 100, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 9:
If we divide 160 by 42, we get 3 and a remainder of 34.
Put 3 as the next digit of the answer. 
Result so far: 206.59523
The remainder is 34 after subtracting 126 from 160.
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 10:
42 can be fit into 340 8 times, resulting in a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 206.595238
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.

On to step 11:
40 divided by 42 is 0 with a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 206.595238
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 12:
42 goes into 400 9 times with a remainder of 22.
Put 9 as the next digit of the answer. 
Result so far: 206.59523809
Subtracting 378 from 400 leaves us 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.

After the division, we end up with 206.59523809 and a remainder of 2.2e-08.