75188 divided by 45 
Our goal is to divide 75188 by 45.

Moving on to step 1:
The number 45 fits into 7 0 times, leaving a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Append the next digit (5) from the dividend to 7 and continue with: 75 / 45

Let's proceed to step 2:
75 divided by 45 is 1 with a remainder of 30.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 30 after subtracting 45 from 75.
Take the next digit (1) from the dividend and append it to 30, then repeat: 301 / 45

On to step 3:
45 can be fit into 301 6 times, resulting in a remainder of 31.
The next digit of our result is 6. 
Result so far: 16.0
The remainder is 31 after subtracting 270 from 301.
Bring next digit (8) of the dividend behind the 31 and repeat the process: 318 / 45

Let's proceed to step 4:
45 can be fit into 318 7 times, resulting in a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 167.0
The remainder is 3 after subtracting 315 from 318.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 45

On to step 5:
38 divided by 45 is 0 with a remainder of 38.
Use 0 as the next digit of our solution. 
Result so far: 1670.0
If we subtract 0 from 38, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 6:
When dividing 380 by 45, we get 8 with a remainder of 20.
Use 8 as the next digit of our solution. 
Result so far: 1670.8
The remainder is 20 after subtracting 360 from 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 7:
The number 45 fits into 200 4 times, leaving a remainder of 20.
Record the quotient 4 as the next digit in the result. 
Result so far: 1670.84
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 8:
The number 45 fits into 200 4 times, leaving a remainder of 20.
Write down 4 as next digit of the result. 
Result so far: 1670.844
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Our division results in 1670.844 with a remaining 0.002.