We're dividing 624638 by 59 
We're looking to find how many times 59 goes into 624638.

On to step 1:
The number 59 fits into 6 0 times, leaving a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (2) from the dividend to 6 and continue with: 62 / 59

Step 2:
When dividing 62 by 59, we get 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 59 from 62 leaves us with 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 59

Going ahead to step 3:
When dividing 34 by 59, we get 0 with a remainder of 34.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Subtracting 0 from 34 leaves us with 34.
Bring next digit (6) of the dividend behind the 34 and repeat the process: 346 / 59

On to step 4:
59 can be fit into 346 5 times, resulting in a remainder of 51.
Write down 5 as next digit of the result. 
Result so far: 105.0
Subtracting 295 from 346 leaves us with 51.
Fetch the next digit (3) from the dividend, attach it to 51 and continue: 513 / 59

Step 5:
59 can be fit into 513 8 times, resulting in a remainder of 41.
Write down 8 as next digit of the result. 
Result so far: 1058.0
If we take 472 away from 513, we end up with 41.
Bring next digit (8) of the dividend behind the 41 and repeat the process: 418 / 59

Going ahead to step 6:
59 can be fit into 418 7 times, resulting in a remainder of 5.
Record the quotient 7 as the next digit in the result. 
Result so far: 10587.0
The remainder is 5 after subtracting 413 from 418.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 7:
59 can be fit into 50 0 times, resulting in a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 10587.0
Subtract 0 from 50 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 8:
The number 59 fits into 500 8 times, leaving a remainder of 28.
Write down 8 as next digit of the result. 
Result so far: 10587.08
Subtracting 472 from 500 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 9:
If we divide 280 by 59, we get 4 and a remainder of 44.
Write down 4 as next digit of the result. 
Result so far: 10587.084
Subtracting 236 from 280 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 10:
59 can be fit into 440 7 times, resulting in a remainder of 27.
Record the quotient 7 as the next digit in the result. 
Result so far: 10587.0847
The remainder is 27 after subtracting 413 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

On to step 11:
270 divided by 59 is 4 with a remainder of 34.
Write down 4 as next digit of the result. 
Result so far: 10587.08474
If we take 236 away from 270, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 12:
340 divided by 59 is 5 with a remainder of 45.
Put 5 as the next digit of the answer. 
Result so far: 10587.084745
Deduct 295 from 340 and we're left with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Let's proceed to step 13:
The number 59 fits into 450 7 times, leaving a remainder of 37.
Put 7 as the next digit of the answer. 
Result so far: 10587.0847457
Deduct 413 from 450 and we're left with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

On to step 14:
370 divided by 59 is 6 with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 10587.08474576
Deduct 354 from 370 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

In conclusion, the division gives 10587.08474576 with a balance of 1.6e-08.