312569 ÷ 30 
Our goal is to divide 312569 by 30.

Step 1:
The number 30 fits into 3 0 times, leaving a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 30

Let's proceed to step 2:
30 can be fit into 31 1 times, resulting in a remainder of 1.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 30 from 31 leaves us with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 30

Moving on to step 3:
If we divide 12 by 30, we get 0 and a remainder of 12.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Subtracting 0 from 12 leaves us with 12.
Grab the next digit (5) from the dividend, add it to 12, then carry on: 125 / 30

Moving on to step 4:
30 can be fit into 125 4 times, resulting in a remainder of 5.
Write down 4 as next digit of the result. 
Result so far: 104.0
If we subtract 120 from 125, we get 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 30

Going ahead to step 5:
If we divide 56 by 30, we get 1 and a remainder of 26.
Record the quotient 1 as the next digit in the result. 
Result so far: 1041.0
If we subtract 30 from 56, we get 26.
Take the next digit (9) from the dividend and append it to 26, then repeat: 269 / 30

Advancing to step 6:
If we divide 269 by 30, we get 8 and a remainder of 29.
Record the quotient 8 as the next digit in the result. 
Result so far: 10418.0
If we subtract 240 from 269, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Let's proceed to step 7:
290 divided by 30 is 9 with a remainder of 20.
The next digit of our result is 9. 
Result so far: 10418.9
Subtracting 270 from 290 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 8:
200 divided by 30 is 6 with a remainder of 20.
Write down 6 as next digit of the result. 
Result so far: 10418.96
If we subtract 180 from 200, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
30 can be fit into 200 6 times, resulting in a remainder of 20.
Put 6 as the next digit of the answer. 
Result so far: 10418.966
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final result is 10418.966 with a remainder of 0.002.