We're dividing 101267 by 75 
We want to figure out the number of times 101267 can be divided by 75.

On to step 1:
If we divide 1 by 75, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 75

Moving on to step 2:
10 divided by 75 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Take the next digit (1) from the dividend and append it to 10, then repeat: 101 / 75

Let's proceed to step 3:
75 can be fit into 101 1 times, resulting in a remainder of 26.
The next digit of our result is 1. 
Result so far: 1.0
If we take 75 away from 101, we end up with 26.
Take the next digit (2) from the dividend and append it to 26, then repeat: 262 / 75

Advancing to step 4:
The number 75 fits into 262 3 times, leaving a remainder of 37.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
Deduct 225 from 262 and we're left with 37.
Append the next digit (6) from the dividend to 37 and continue with: 376 / 75

Let's proceed to step 5:
75 goes into 376 5 times with a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 135.0
Deduct 375 from 376 and we're left with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 75

Moving on to step 6:
75 can be fit into 17 0 times, resulting in a remainder of 17.
Put 0 as the next digit of the answer. 
Result so far: 1350.0
If we subtract 0 from 17, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Step 7:
75 goes into 170 2 times with a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 1350.2
Subtract 150 from 170 to get 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:
200 divided by 75 is 2 with a remainder of 50.
The next digit of our result is 2. 
Result so far: 1350.22
If we take 150 away from 200, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The quotient of the division is 1350.22, and the remainder is 0.05.