We look at the division of 583278 by 59 
Our goal is to divide 583278 by 59.

Moving on to step 1:
When dividing 5 by 59, we get 0 with 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.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 59

Advancing to step 2:
The number 59 fits into 58 0 times, leaving a remainder of 58.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 58, we get 58.
Grab the next digit (3) from the dividend, add it to 58, then carry on: 583 / 59

Step 3:
583 divided by 59 is 9 with a remainder of 52.
Write down 9 as next digit of the result. 
Result so far: 9.0
The remainder is 52 after subtracting 531 from 583.
Fetch the next digit (2) from the dividend, attach it to 52 and continue: 522 / 59

Let's proceed to step 4:
59 can be fit into 522 8 times, resulting in a remainder of 50.
Put 8 as the next digit of the answer. 
Result so far: 98.0
Subtract 472 from 522 to get 50.
Take the next digit (7) from the dividend and append it to 50, then repeat: 507 / 59

Moving on to step 5:
When dividing 507 by 59, we get 8 with a remainder of 35.
The number 8 becomes the next digit in our result. 
Result so far: 988.0
If we take 472 away from 507, we end up with 35.
Include the next digit (8) from the dividend after 35, then repeat: 358 / 59

On to step 6:
If we divide 358 by 59, we get 6 and a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 9886.0
Subtract 354 from 358 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 7:
59 goes into 40 0 times with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 9886.0
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 8:
400 divided by 59 is 6 with a remainder of 46.
The next digit of our result is 6. 
Result so far: 9886.06
Deduct 354 from 400 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 9:
If we divide 460 by 59, we get 7 and a remainder of 47.
Put 7 as the next digit of the answer. 
Result so far: 9886.067
Subtract 413 from 460 to 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.

Going ahead to step 10:
59 goes into 470 7 times with a remainder of 57.
Write down 7 as next digit of the result. 
Result so far: 9886.0677
If we take 413 away from 470, we end up with 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 result is 9886.0677 with a remainder of 0.00057.