We're dividing 3413981 by 581 
We're looking to find how many times 581 goes into 3413981.

Advancing to step 1:
581 can be fit into 3 0 times, resulting in a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 581

Step 2:
If we divide 34 by 581, we get 0 and a remainder of 34.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 34 leaves us with 34.
Bring next digit (1) of the dividend behind the 34 and repeat the process: 341 / 581

Step 3:
When dividing 341 by 581, we get 0 with a remainder of 341.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 341, we end up with 341.
Take the next digit (3) from the dividend and append it to 341, then repeat: 3413 / 581

Let's proceed to step 4:
If we divide 3413 by 581, we get 5 and a remainder of 508.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Deduct 2905 from 3413 and we're left with 508.
Append the next digit (9) from the dividend to 508 and continue with: 5089 / 581

Going ahead to step 5:
If we divide 5089 by 581, we get 8 and a remainder of 441.
Write down 8 as next digit of the result. 
Result so far: 58.0
Subtracting 4648 from 5089 leaves us with 441.
Append the next digit (8) from the dividend to 441 and continue with: 4418 / 581

Let's proceed to step 6:
If we divide 4418 by 581, we get 7 and a remainder of 351.
The next digit of our result is 7. 
Result so far: 587.0
If we take 4067 away from 4418, we end up with 351.
Bring next digit (1) of the dividend behind the 351 and repeat the process: 3511 / 581

Step 7:
When dividing 3511 by 581, we get 6 with a remainder of 25.
Put 6 as the next digit of the answer. 
Result so far: 5876.0
If we take 3486 away from 3511, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 8:
581 goes into 250 0 times with a remainder of 250.
Use 0 as the next digit of our solution. 
Result so far: 5876.0
If we subtract 0 from 250, we get 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2500, and continue the process.

Let's proceed to step 9:
The number 581 fits into 2500 4 times, leaving a remainder of 176.
The number 4 becomes the next digit in our result. 
Result so far: 5876.04
Subtract 2324 from 2500 to get 176.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1760, and continue the process.

Moving on to step 10:
When dividing 1760 by 581, we get 3 with a remainder of 17.
Record the quotient 3 as the next digit in the result. 
Result so far: 5876.043
If we take 1743 away from 1760, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 11:
581 can be fit into 170 0 times, resulting in a remainder of 170.
Record the quotient 0 as the next digit in the result. 
Result so far: 5876.043
If we take 0 away from 170, we end up with 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1700, and continue the process.

Step 12:
581 can be fit into 1700 2 times, resulting in a remainder of 538.
Record the quotient 2 as the next digit in the result. 
Result so far: 5876.04302
Subtract 1162 from 1700 to get 538.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5380, and continue the process.

Advancing to step 13:
When dividing 5380 by 581, we get 9 with a remainder of 151.
Put 9 as the next digit of the answer. 
Result so far: 5876.043029
If we take 5229 away from 5380, we end up with 151.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1510, and continue the process.

Step 14:
The number 581 fits into 1510 2 times, leaving a remainder of 348.
Use 2 as the next digit of our solution. 
Result so far: 5876.0430292
Deduct 1162 from 1510 and we're left with 348.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3480, and continue the process.

Advancing to step 15:
The number 581 fits into 3480 5 times, leaving a remainder of 575.
Put 5 as the next digit of the answer. 
Result so far: 5876.04302925
The remainder is 575 after subtracting 2905 from 3480.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5750, and continue the process.

After the division, we end up with 5876.04302925 and a remainder of 5.75e-07.