682638 divided by 59 
We're looking to find how many times 59 goes into 682638.

Let's proceed to step 1:
59 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 59

On to step 2:
If we divide 68 by 59, we get 1 and a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 59 from 68, we get 9.
Append the next digit (2) from the dividend to 9 and continue with: 92 / 59

Moving on to step 3:
59 goes into 92 1 times with a remainder of 33.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
The remainder is 33 after subtracting 59 from 92.
Grab the next digit (6) from the dividend, add it to 33, then carry on: 336 / 59

Let's proceed to step 4:
59 goes into 336 5 times with a remainder of 41.
Write down 5 as next digit of the result. 
Result so far: 115.0
The remainder is 41 after subtracting 295 from 336.
Fetch the next digit (3) from the dividend, attach it to 41 and continue: 413 / 59

Going ahead to step 5:
59 can be fit into 413 7 times, resulting in a remainder of 0.
The next digit of our result is 7. 
Result so far: 1157.0
The remainder is 0 after subtracting 413 from 413.
Include the next digit (8) from the dividend after 0, then repeat: 8 / 59

Step 6:
8 divided by 59 is 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 11570.0
Subtract 0 from 8 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.

Step 7:
80 divided by 59 is 1 with a remainder of 21.
Write down 1 as next digit of the result. 
Result so far: 11570.1
If we subtract 59 from 80, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 8:
59 goes into 210 3 times with a remainder of 33.
The next digit of our result is 3. 
Result so far: 11570.13
Deduct 177 from 210 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

On to step 9:
59 goes into 330 5 times with a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 11570.135
The remainder is 35 after subtracting 295 from 330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 10:
59 goes into 350 5 times with a remainder of 55.
The number 5 becomes the next digit in our result. 
Result so far: 11570.1355
If we subtract 295 from 350, we get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

The quotient of the division is 11570.1355, and the remainder is 0.00055.