We look at the division of 31677 by 75 
We want to figure out the number of times 31677 can be divided by 75.

Moving on to step 1:
75 goes into 3 0 times with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (1) from the dividend and append it to 3, then repeat: 31 / 75

Let's proceed to step 2:
31 divided by 75 is 0 with a remainder of 31.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 31 leaves us with 31.
Fetch the next digit (6) from the dividend, attach it to 31 and continue: 316 / 75

On to step 3:
75 goes into 316 4 times with a remainder of 16.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Subtract 300 from 316 to get 16.
Take the next digit (7) from the dividend and append it to 16, then repeat: 167 / 75

Moving on to step 4:
The number 75 fits into 167 2 times, leaving a remainder of 17.
Put 2 as the next digit of the answer. 
Result so far: 42.0
If we take 150 away from 167, we end up with 17.
Take the next digit (7) from the dividend and append it to 17, then repeat: 177 / 75

Let's proceed to step 5:
If we divide 177 by 75, we get 2 and a remainder of 27.
Use 2 as the next digit of our solution. 
Result so far: 422.0
Subtracting 150 from 177 leaves us with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 6:
75 goes into 270 3 times with a remainder of 45.
Use 3 as the next digit of our solution. 
Result so far: 422.3
If we subtract 225 from 270, we get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Let's proceed to step 7:
If we divide 450 by 75, we get 6 and a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 422.36
Subtract 450 from 450 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 8:
75 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 422.36
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 9:
When dividing 0 by 75, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 422.36
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final result is 422.36 with a remainder of 0.0.