We look at the division of 35522589 by 588 
We want to figure out the number of times 35522589 can be divided by 588.

Step 1:
The number 588 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 588

Advancing to step 2:
35 divided by 588 is 0 with a remainder of 35.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 35 to get 35.
Grab the next digit (5) from the dividend, add it to 35, then carry on: 355 / 588

Going ahead to step 3:
The number 588 fits into 355 0 times, leaving a remainder of 355.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 355, we get 355.
Take the next digit (2) from the dividend and append it to 355, then repeat: 3552 / 588

Step 4:
588 goes into 3552 6 times with a remainder of 24.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 24 after subtracting 3528 from 3552.
Append the next digit (2) from the dividend to 24 and continue with: 242 / 588

Advancing to step 5:
When dividing 242 by 588, we get 0 with a remainder of 242.
Write down 0 as next digit of the result. 
Result so far: 60.0
Deduct 0 from 242 and we're left with 242.
Append the next digit (5) from the dividend to 242 and continue with: 2425 / 588

On to step 6:
588 can be fit into 2425 4 times, resulting in a remainder of 73.
Put 4 as the next digit of the answer. 
Result so far: 604.0
Subtract 2352 from 2425 to get 73.
Take the next digit (8) from the dividend and append it to 73, then repeat: 738 / 588

Going ahead to step 7:
When dividing 738 by 588, we get 1 with a remainder of 150.
The next digit of our result is 1. 
Result so far: 6041.0
If we subtract 588 from 738, we get 150.
Grab the next digit (9) from the dividend, add it to 150, then carry on: 1509 / 588

Let's proceed to step 8:
588 goes into 1509 2 times with a remainder of 333.
The number 2 becomes the next digit in our result. 
Result so far: 60412.0
Subtract 1176 from 1509 to get 333.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3330, and continue the process.

Going ahead to step 9:
588 goes into 3330 5 times with a remainder of 390.
Write down 5 as next digit of the result. 
Result so far: 60412.5
Deduct 2940 from 3330 and we're left with 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3900, and continue the process.

Advancing to step 10:
588 goes into 3900 6 times with a remainder of 372.
The number 6 becomes the next digit in our result. 
Result so far: 60412.56
Subtracting 3528 from 3900 leaves us with 372.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3720, and continue the process.

Moving on to step 11:
588 can be fit into 3720 6 times, resulting in a remainder of 192.
The next digit of our result is 6. 
Result so far: 60412.566
Deduct 3528 from 3720 and we're left with 192.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1920, and continue the process.

The final outcome is 60412.566, with a leftover of 0.0192.