765566 divided by 31 
Our goal is to divide 765566 by 31.

Step 1:
7 divided by 31 is 0 with a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 31

Moving on to step 2:
When dividing 76 by 31, we get 2 with a remainder of 14.
The next digit of our result is 2. 
Result so far: 2.0
Subtract 62 from 76 to get 14.
Bring next digit (5) of the dividend behind the 14 and repeat the process: 145 / 31

Step 3:
145 divided by 31 is 4 with a remainder of 21.
The next digit of our result is 4. 
Result so far: 24.0
Deduct 124 from 145 and we're left with 21.
Fetch the next digit (5) from the dividend, attach it to 21 and continue: 215 / 31

Going ahead to step 4:
31 can be fit into 215 6 times, resulting in a remainder of 29.
Record the quotient 6 as the next digit in the result. 
Result so far: 246.0
Deduct 186 from 215 and we're left with 29.
Append the next digit (6) from the dividend to 29 and continue with: 296 / 31

Going ahead to step 5:
When dividing 296 by 31, we get 9 with a remainder of 17.
The next digit of our result is 9. 
Result so far: 2469.0
The remainder is 17 after subtracting 279 from 296.
Append the next digit (6) from the dividend to 17 and continue with: 176 / 31

Moving on to step 6:
When dividing 176 by 31, we get 5 with a remainder of 21.
Write down 5 as next digit of the result. 
Result so far: 24695.0
Subtracting 155 from 176 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 7:
If we divide 210 by 31, we get 6 and a remainder of 24.
Write down 6 as next digit of the result. 
Result so far: 24695.6
If we subtract 186 from 210, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 8:
240 divided by 31 is 7 with a remainder of 23.
Write down 7 as next digit of the result. 
Result so far: 24695.67
Deduct 217 from 240 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 9:
If we divide 230 by 31, we get 7 and a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 24695.677
Subtracting 217 from 230 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

After the division, we end up with 24695.677 and a remainder of 0.0013.