We're dividing 508213 by 77 
We want to figure out the number of times 508213 can be divided by 77.

Step 1:
When dividing 5 by 77, we get 0 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.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 77

Let's proceed to step 2:
77 goes into 50 0 times with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 50, we get 50.
Include the next digit (8) from the dividend after 50, then repeat: 508 / 77

Moving on to step 3:
77 can be fit into 508 6 times, resulting in a remainder of 46.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Deduct 462 from 508 and we're left with 46.
Fetch the next digit (2) from the dividend, attach it to 46 and continue: 462 / 77

Moving on to step 4:
The number 77 fits into 462 6 times, leaving a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 66.0
If we subtract 462 from 462, we get 0.
Fetch the next digit (1) from the dividend, attach it to 0 and continue: 1 / 77

Moving on to step 5:
If we divide 1 by 77, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 660.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 77

Let's proceed to step 6:
77 can be fit into 13 0 times, resulting in a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 6600.0
The remainder is 13 after subtracting 0 from 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 7:
If we divide 130 by 77, we get 1 and a remainder of 53.
The next digit of our result is 1. 
Result so far: 6600.1
Subtract 77 from 130 to get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Going ahead to step 8:
77 goes into 530 6 times with a remainder of 68.
Use 6 as the next digit of our solution. 
Result so far: 6600.16
If we take 462 away from 530, we end up with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Advancing to step 9:
If we divide 680 by 77, we get 8 and a remainder of 64.
The number 8 becomes the next digit in our result. 
Result so far: 6600.168
The remainder is 64 after subtracting 616 from 680.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Advancing to step 10:
640 divided by 77 is 8 with a remainder of 24.
The number 8 becomes the next digit in our result. 
Result so far: 6600.1688
Deduct 616 from 640 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The final result is 6600.1688 with a remainder of 0.00024.