509098 ÷ 59 
We want to figure out the number of times 509098 can be divided by 59.

On to step 1:
If we divide 5 by 59, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 59

On to step 2:
If we divide 50 by 59, we get 0 and a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Grab the next digit (9) from the dividend, add it to 50, then carry on: 509 / 59

Going ahead to step 3:
When dividing 509 by 59, we get 8 with a remainder of 37.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Subtract 472 from 509 to get 37.
Take the next digit (0) from the dividend and append it to 37, then repeat: 370 / 59

Going ahead to step 4:
If we divide 370 by 59, we get 6 and a remainder of 16.
Use 6 as the next digit of our solution. 
Result so far: 86.0
Deduct 354 from 370 and we're left with 16.
Fetch the next digit (9) from the dividend, attach it to 16 and continue: 169 / 59

Advancing to step 5:
When dividing 169 by 59, we get 2 with a remainder of 51.
Use 2 as the next digit of our solution. 
Result so far: 862.0
The remainder is 51 after subtracting 118 from 169.
Fetch the next digit (8) from the dividend, attach it to 51 and continue: 518 / 59

Advancing to step 6:
If we divide 518 by 59, we get 8 and a remainder of 46.
Record the quotient 8 as the next digit in the result. 
Result so far: 8628.0
If we subtract 472 from 518, we get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 7:
460 divided by 59 is 7 with a remainder of 47.
Write down 7 as next digit of the result. 
Result so far: 8628.7
If we subtract 413 from 460, we get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Let's proceed to step 8:
470 divided by 59 is 7 with a remainder of 57.
The number 7 becomes the next digit in our result. 
Result so far: 8628.77
Subtract 413 from 470 to get 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

The final outcome is 8628.77, with a leftover of 0.057.