145666 ÷ 90 
Our goal is to divide 145666 by 90.

Step 1:
90 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Grab the next digit (4) from the dividend, add it to 1, then carry on: 14 / 90

Going ahead to step 2:
The number 90 fits into 14 0 times, leaving a remainder of 14.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 14 and we're left with 14.
Bring next digit (5) of the dividend behind the 14 and repeat the process: 145 / 90

Let's proceed to step 3:
90 goes into 145 1 times with a remainder of 55.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 90 from 145 leaves us with 55.
Take the next digit (6) from the dividend and append it to 55, then repeat: 556 / 90

On to step 4:
90 goes into 556 6 times with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 16.0
If we take 540 away from 556, we end up with 16.
Fetch the next digit (6) from the dividend, attach it to 16 and continue: 166 / 90

Moving on to step 5:
If we divide 166 by 90, we get 1 and a remainder of 76.
Write down 1 as next digit of the result. 
Result so far: 161.0
Deduct 90 from 166 and we're left with 76.
Grab the next digit (6) from the dividend, add it to 76, then carry on: 766 / 90

Moving on to step 6:
If we divide 766 by 90, we get 8 and a remainder of 46.
Write down 8 as next digit of the result. 
Result so far: 1618.0
If we subtract 720 from 766, 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.

Step 7:
460 divided by 90 is 5 with a remainder of 10.
The next digit of our result is 5. 
Result so far: 1618.5
The remainder is 10 after subtracting 450 from 460.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 8:
90 can be fit into 100 1 times, resulting in a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 1618.51
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.

Advancing to step 9:
90 can be fit into 100 1 times, resulting in a remainder of 10.
The next digit of our result is 1. 
Result so far: 1618.511
If we subtract 90 from 100, 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.

The quotient of the division is 1618.511, and the remainder is 0.001.