506121 ÷ 8 
We want to figure out the number of times 506121 can be divided by 8.

Step 1:
8 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 8

On to step 2:
8 can be fit into 50 6 times, resulting in a remainder of 2.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 2 after subtracting 48 from 50.
Fetch the next digit (6) from the dividend, attach it to 2 and continue: 26 / 8

Let's proceed to step 3:
When dividing 26 by 8, we get 3 with a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 63.0
Deduct 24 from 26 and we're left with 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 8

On to step 4:
8 can be fit into 21 2 times, resulting in a remainder of 5.
Use 2 as the next digit of our solution. 
Result so far: 632.0
Deduct 16 from 21 and we're left with 5.
Grab the next digit (2) from the dividend, add it to 5, then carry on: 52 / 8

Let's proceed to step 5:
The number 8 fits into 52 6 times, leaving a remainder of 4.
The next digit of our result is 6. 
Result so far: 6326.0
If we take 48 away from 52, we end up with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 8

Going ahead to step 6:
The number 8 fits into 41 5 times, leaving a remainder of 1.
Put 5 as the next digit of the answer. 
Result so far: 63265.0
Deduct 40 from 41 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
8 can be fit into 10 1 times, resulting in a remainder of 2.
The next digit of our result is 1. 
Result so far: 63265.1
If we subtract 8 from 10, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
The number 8 fits into 20 2 times, leaving a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 63265.12
Subtract 16 from 20 to 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.

Let's proceed to step 9:
40 divided by 8 is 5 with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 63265.125
The remainder is 0 after subtracting 40 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 10:
The number 8 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 63265.125
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.

Advancing to step 11:
When dividing 0 by 8, we get 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 63265.125
Subtracting 0 from 0 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.

In conclusion, the division gives 63265.125 with a balance of 0.0.