300420 ÷ 8 
We want to figure out the number of times 300420 can be divided by 8.

On to step 1:
If we divide 3 by 8, we get 0 and a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Grab the next digit (0) from the dividend, add it to 3, then carry on: 30 / 8

Going ahead to step 2:
If we divide 30 by 8, we get 3 and a remainder of 6.
The next digit of our result is 3. 
Result so far: 3.0
Subtracting 24 from 30 leaves us with 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 8

Let's proceed to step 3:
If we divide 60 by 8, we get 7 and a remainder of 4.
Use 7 as the next digit of our solution. 
Result so far: 37.0
If we subtract 56 from 60, we get 4.
Include the next digit (4) from the dividend after 4, then repeat: 44 / 8

Moving on to step 4:
If we divide 44 by 8, we get 5 and a remainder of 4.
Record the quotient 5 as the next digit in the result. 
Result so far: 375.0
The remainder is 4 after subtracting 40 from 44.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 8

On to step 5:
The number 8 fits into 42 5 times, leaving a remainder of 2.
The next digit of our result is 5. 
Result so far: 3755.0
Deduct 40 from 42 and we're left with 2.
Append the next digit (0) from the dividend to 2 and continue with: 20 / 8

Let's proceed to step 6:
8 goes into 20 2 times with a remainder of 4.
The next digit of our result is 2. 
Result so far: 37552.0
Deduct 16 from 20 and we're left 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.

Step 7:
8 goes into 40 5 times with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 37552.5
Subtract 40 from 40 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 8:
8 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 37552.5
If we take 0 away from 0, we end up 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 9:
0 divided by 8 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 37552.5
Deduct 0 from 0 and we're left 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.

The final result is 37552.5 with a remainder of 0.0.