We're dividing 580129 by 61 
Let's see how many times 61 fits into 580129.

Moving on to step 1:
When dividing 5 by 61, we get 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 61

Let's proceed to step 2:
61 can be fit into 58 0 times, resulting in a remainder of 58.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 58 leaves us with 58.
Include the next digit (0) from the dividend after 58, then repeat: 580 / 61

On to step 3:
The number 61 fits into 580 9 times, leaving a remainder of 31.
The next digit of our result is 9. 
Result so far: 9.0
Subtract 549 from 580 to get 31.
Bring next digit (1) of the dividend behind the 31 and repeat the process: 311 / 61

Let's proceed to step 4:
61 goes into 311 5 times with a remainder of 6.
The next digit of our result is 5. 
Result so far: 95.0
Subtracting 305 from 311 leaves us with 6.
Append the next digit (2) from the dividend to 6 and continue with: 62 / 61

Advancing to step 5:
If we divide 62 by 61, we get 1 and a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 951.0
If we subtract 61 from 62, we get 1.
Take the next digit (9) from the dividend and append it to 1, then repeat: 19 / 61

Advancing to step 6:
When dividing 19 by 61, we get 0 with a remainder of 19.
Use 0 as the next digit of our solution. 
Result so far: 9510.0
Subtracting 0 from 19 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Step 7:
If we divide 190 by 61, we get 3 and a remainder of 7.
Use 3 as the next digit of our solution. 
Result so far: 9510.3
Subtract 183 from 190 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.

Advancing to step 8:
When dividing 70 by 61, we get 1 with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 9510.31
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.

On to step 9:
When dividing 90 by 61, we get 1 with a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 9510.311
Deduct 61 from 90 and we're left 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.

The quotient of the division is 9510.311, and the remainder is 0.0029.