We're dividing 646593 by 61 
Our goal is to divide 646593 by 61.

Advancing to step 1:
If we divide 6 by 61, we get 0 and a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 61

Moving on to step 2:
61 goes into 64 1 times with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 61 from 64 leaves us with 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 61

Moving on to step 3:
The number 61 fits into 36 0 times, leaving a remainder of 36.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
If we take 0 away from 36, we end up with 36.
Include the next digit (5) from the dividend after 36, then repeat: 365 / 61

On to step 4:
365 divided by 61 is 5 with a remainder of 60.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
If we take 305 away from 365, we end up with 60.
Fetch the next digit (9) from the dividend, attach it to 60 and continue: 609 / 61

Going ahead to step 5:
The number 61 fits into 609 9 times, leaving a remainder of 60.
Put 9 as the next digit of the answer. 
Result so far: 1059.0
Deduct 549 from 609 and we're left with 60.
Include the next digit (3) from the dividend after 60, then repeat: 603 / 61

Let's proceed to step 6:
61 can be fit into 603 9 times, resulting in a remainder of 54.
Use 9 as the next digit of our solution. 
Result so far: 10599.0
If we take 549 away from 603, we end up with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Advancing to step 7:
When dividing 540 by 61, we get 8 with a remainder of 52.
The next digit of our result is 8. 
Result so far: 10599.8
If we subtract 488 from 540, we get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 8:
520 divided by 61 is 8 with a remainder of 32.
Record the quotient 8 as the next digit in the result. 
Result so far: 10599.88
The remainder is 32 after subtracting 488 from 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The final result is 10599.88 with a remainder of 0.032.