We're dividing 5108529 by 581 
We're looking to find how many times 581 goes into 5108529.

Going ahead to step 1:
If we divide 5 by 581, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 581

Advancing to step 2:
581 goes into 51 0 times with a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 51 leaves us with 51.
Fetch the next digit (0) from the dividend, attach it to 51 and continue: 510 / 581

Step 3:
581 can be fit into 510 0 times, resulting in a remainder of 510.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 510 to get 510.
Grab the next digit (8) from the dividend, add it to 510, then carry on: 5108 / 581

Advancing to step 4:
The number 581 fits into 5108 8 times, leaving a remainder of 460.
Write down 8 as next digit of the result. 
Result so far: 8.0
The remainder is 460 after subtracting 4648 from 5108.
Fetch the next digit (5) from the dividend, attach it to 460 and continue: 4605 / 581

Advancing to step 5:
When dividing 4605 by 581, we get 7 with a remainder of 538.
The number 7 becomes the next digit in our result. 
Result so far: 87.0
If we subtract 4067 from 4605, we get 538.
Take the next digit (2) from the dividend and append it to 538, then repeat: 5382 / 581

Let's proceed to step 6:
581 goes into 5382 9 times with a remainder of 153.
The number 9 becomes the next digit in our result. 
Result so far: 879.0
Subtract 5229 from 5382 to get 153.
Append the next digit (9) from the dividend to 153 and continue with: 1539 / 581

Going ahead to step 7:
When dividing 1539 by 581, we get 2 with a remainder of 377.
The next digit of our result is 2. 
Result so far: 8792.0
If we subtract 1162 from 1539, we get 377.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3770, and continue the process.

Let's proceed to step 8:
The number 581 fits into 3770 6 times, leaving a remainder of 284.
Write down 6 as next digit of the result. 
Result so far: 8792.6
Subtract 3486 from 3770 to get 284.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2840, and continue the process.

Moving on to step 9:
If we divide 2840 by 581, we get 4 and a remainder of 516.
The next digit of our result is 4. 
Result so far: 8792.64
Subtracting 2324 from 2840 leaves us with 516.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5160, and continue the process.

On to step 10:
If we divide 5160 by 581, we get 8 and a remainder of 512.
Write down 8 as next digit of the result. 
Result so far: 8792.648
Subtracting 4648 from 5160 leaves us with 512.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5120, and continue the process.

On to step 11:
581 can be fit into 5120 8 times, resulting in a remainder of 472.
Use 8 as the next digit of our solution. 
Result so far: 8792.6488
The remainder is 472 after subtracting 4648 from 5120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4720, and continue the process.

The final result is 8792.6488 with a remainder of 0.00472.