We're dividing 624331 by 59 
We want to figure out the number of times 624331 can be divided by 59.

On to step 1:
The number 59 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Bring next digit (2) of the dividend behind the 6 and repeat the process: 62 / 59

On to step 2:
59 can be fit into 62 1 times, resulting in a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 59 from 62, we get 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 59

Moving on to step 3:
If we divide 34 by 59, we get 0 and a remainder of 34.
The next digit of our result is 0. 
Result so far: 10.0
Subtract 0 from 34 to get 34.
Take the next digit (3) from the dividend and append it to 34, then repeat: 343 / 59

Step 4:
If we divide 343 by 59, we get 5 and a remainder of 48.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
Subtracting 295 from 343 leaves us with 48.
Include the next digit (3) from the dividend after 48, then repeat: 483 / 59

Step 5:
483 divided by 59 is 8 with a remainder of 11.
Write down 8 as next digit of the result. 
Result so far: 1058.0
Deduct 472 from 483 and we're left with 11.
Take the next digit (1) from the dividend and append it to 11, then repeat: 111 / 59

Step 6:
59 can be fit into 111 1 times, resulting in a remainder of 52.
Record the quotient 1 as the next digit in the result. 
Result so far: 10581.0
Deduct 59 from 111 and we're left with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 7:
When dividing 520 by 59, we get 8 with a remainder of 48.
Put 8 as the next digit of the answer. 
Result so far: 10581.8
Subtract 472 from 520 to get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 8:
When dividing 480 by 59, we get 8 with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 10581.88
Subtract 472 from 480 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The final outcome is 10581.88, with a leftover of 0.008.