We're dividing 542669 by 8 
We want to figure out the number of times 542669 can be divided by 8.

On to step 1:
8 can be fit into 5 0 times, resulting in a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (4) from the dividend and append it to 5, then repeat: 54 / 8

Going ahead to step 2:
8 goes into 54 6 times with a remainder of 6.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 6 after subtracting 48 from 54.
Fetch the next digit (2) from the dividend, attach it to 6 and continue: 62 / 8

Step 3:
8 goes into 62 7 times with a remainder of 6.
The next digit of our result is 7. 
Result so far: 67.0
Deduct 56 from 62 and we're left with 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 8

Going ahead to step 4:
8 goes into 66 8 times with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 678.0
Subtracting 64 from 66 leaves us with 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 8

Moving on to step 5:
8 goes into 26 3 times with a remainder of 2.
The next digit of our result is 3. 
Result so far: 6783.0
Subtracting 24 from 26 leaves us with 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 8

Advancing to step 6:
When dividing 29 by 8, we get 3 with a remainder of 5.
The next digit of our result is 3. 
Result so far: 67833.0
The remainder is 5 after subtracting 24 from 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 7:
When dividing 50 by 8, we get 6 with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 67833.6
Deduct 48 from 50 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
The number 8 fits into 20 2 times, leaving a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 67833.62
If we subtract 16 from 20, we get 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 9:
The number 8 fits into 40 5 times, leaving a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 67833.625
Subtracting 40 from 40 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 10:
If we divide 0 by 8, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 67833.625
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 11:
8 can be fit into 0 0 times, resulting in a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 67833.625
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 67833.625 and a remainder of 0.0.