Let's divide 15666 by 45
Our goal is to divide 15666 by 45.

Let's proceed to step 1:
1 divided by 45 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 45

Going ahead to step 2:
If we divide 15 by 45, we get 0 and a remainder of 15.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 15, we end up with 15.
Bring next digit (6) of the dividend behind the 15 and repeat the process: 156 / 45

Advancing to step 3:
When dividing 156 by 45, we get 3 with a remainder of 21.
Put 3 as the next digit of the answer. 
Result so far: 3.0
The remainder is 21 after subtracting 135 from 156.
Fetch the next digit (6) from the dividend, attach it to 21 and continue: 216 / 45

Let's proceed to step 4:
45 can be fit into 216 4 times, resulting in a remainder of 36.
Record the quotient 4 as the next digit in the result. 
Result so far: 34.0
If we subtract 180 from 216, we get 36.
Grab the next digit (6) from the dividend, add it to 36, then carry on: 366 / 45

Moving on to step 5:
When dividing 366 by 45, we get 8 with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 348.0
Subtract 360 from 366 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 6:
45 can be fit into 60 1 times, resulting in a remainder of 15.
Write down 1 as next digit of the result. 
Result so far: 348.1
If we subtract 45 from 60, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 7:
45 goes into 150 3 times with a remainder of 15.
The next digit of our result is 3. 
Result so far: 348.13
Subtract 135 from 150 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 8:
45 can be fit into 150 3 times, resulting in a remainder of 15.
Use 3 as the next digit of our solution. 
Result so far: 348.133
Subtracting 135 from 150 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Our division results in 348.133 with a remaining 0.0015.