557254 ÷ 90 
We want to figure out the number of times 557254 can be divided by 90.

Step 1:
When dividing 5 by 90, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 90

On to step 2:
When dividing 55 by 90, we get 0 with a remainder of 55.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Include the next digit (7) from the dividend after 55, then repeat: 557 / 90

Step 3:
When dividing 557 by 90, we get 6 with a remainder of 17.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we subtract 540 from 557, we get 17.
Bring next digit (2) of the dividend behind the 17 and repeat the process: 172 / 90

Advancing to step 4:
When dividing 172 by 90, we get 1 with a remainder of 82.
The number 1 becomes the next digit in our result. 
Result so far: 61.0
If we subtract 90 from 172, we get 82.
Bring next digit (5) of the dividend behind the 82 and repeat the process: 825 / 90

Going ahead to step 5:
90 can be fit into 825 9 times, resulting in a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 619.0
Subtract 810 from 825 to get 15.
Take the next digit (4) from the dividend and append it to 15, then repeat: 154 / 90

Let's proceed to step 6:
90 goes into 154 1 times with a remainder of 64.
Put 1 as the next digit of the answer. 
Result so far: 6191.0
Subtracting 90 from 154 leaves us with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

On to step 7:
If we divide 640 by 90, we get 7 and a remainder of 10.
Put 7 as the next digit of the answer. 
Result so far: 6191.7
If we subtract 630 from 640, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
90 can be fit into 100 1 times, resulting in a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 6191.71
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 9:
If we divide 100 by 90, we get 1 and a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 6191.711
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 6191.711, and the remainder is 0.001.