Let's divide 586034 by 61
Our goal is to divide 586034 by 61.

Advancing to step 1:
When dividing 5 by 61, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 61

Step 2:
61 goes into 58 0 times with a remainder of 58.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 58 after subtracting 0 from 58.
Take the next digit (6) from the dividend and append it to 58, then repeat: 586 / 61

Step 3:
If we divide 586 by 61, we get 9 and a remainder of 37.
Use 9 as the next digit of our solution. 
Result so far: 9.0
Subtract 549 from 586 to get 37.
Take the next digit (0) from the dividend and append it to 37, then repeat: 370 / 61

Let's proceed to step 4:
The number 61 fits into 370 6 times, leaving a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 96.0
Subtract 366 from 370 to get 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 61

On to step 5:
If we divide 43 by 61, we get 0 and a remainder of 43.
The number 0 becomes the next digit in our result. 
Result so far: 960.0
If we take 0 away from 43, we end up with 43.
Include the next digit (4) from the dividend after 43, then repeat: 434 / 61

Let's proceed to step 6:
The number 61 fits into 434 7 times, leaving a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 9607.0
Subtract 427 from 434 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 7:
61 goes into 70 1 times with a remainder of 9.
The next digit of our result is 1. 
Result so far: 9607.1
If we take 61 away from 70, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 8:
If we divide 90 by 61, we get 1 and a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 9607.11
Subtract 61 from 90 to 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.

Our division results in 9607.11 with a remaining 0.029.