We look at the division of 581974 by 65 
Let's see how many times 65 fits into 581974.

Moving on to step 1:
When dividing 5 by 65, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 65

Advancing to step 2:
When dividing 58 by 65, we get 0 with a remainder of 58.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 58 and we're left with 58.
Bring next digit (1) of the dividend behind the 58 and repeat the process: 581 / 65

Step 3:
The number 65 fits into 581 8 times, leaving a remainder of 61.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Subtract 520 from 581 to get 61.
Bring next digit (9) of the dividend behind the 61 and repeat the process: 619 / 65

Moving on to step 4:
If we divide 619 by 65, we get 9 and a remainder of 34.
Put 9 as the next digit of the answer. 
Result so far: 89.0
Subtracting 585 from 619 leaves us with 34.
Append the next digit (7) from the dividend to 34 and continue with: 347 / 65

Moving on to step 5:
If we divide 347 by 65, we get 5 and a remainder of 22.
The next digit of our result is 5. 
Result so far: 895.0
If we take 325 away from 347, we end up with 22.
Fetch the next digit (4) from the dividend, attach it to 22 and continue: 224 / 65

Moving on to step 6:
65 goes into 224 3 times with a remainder of 29.
Put 3 as the next digit of the answer. 
Result so far: 8953.0
If we take 195 away from 224, we end up with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Going ahead to step 7:
65 goes into 290 4 times with a remainder of 30.
Put 4 as the next digit of the answer. 
Result so far: 8953.4
If we take 260 away from 290, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
When dividing 300 by 65, we get 4 with a remainder of 40.
The number 4 becomes the next digit in our result. 
Result so far: 8953.44
Subtracting 260 from 300 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The final result is 8953.44 with a remainder of 0.04.