We're dividing 100279 by 75 
We want to figure out the number of times 100279 can be divided by 75.

Step 1:
The number 75 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 75

Going ahead to step 2:
75 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Fetch the next digit (0) from the dividend, attach it to 10 and continue: 100 / 75

Going ahead to step 3:
75 goes into 100 1 times with a remainder of 25.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 75 from 100 to get 25.
Append the next digit (2) from the dividend to 25 and continue with: 252 / 75

Let's proceed to step 4:
When dividing 252 by 75, we get 3 with a remainder of 27.
Write down 3 as next digit of the result. 
Result so far: 13.0
If we take 225 away from 252, we end up with 27.
Grab the next digit (7) from the dividend, add it to 27, then carry on: 277 / 75

On to step 5:
If we divide 277 by 75, we get 3 and a remainder of 52.
Write down 3 as next digit of the result. 
Result so far: 133.0
If we subtract 225 from 277, we get 52.
Grab the next digit (9) from the dividend, add it to 52, then carry on: 529 / 75

Let's proceed to step 6:
When dividing 529 by 75, we get 7 with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 1337.0
If we take 525 away from 529, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 7:
If we divide 40 by 75, we get 0 and a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 1337.0
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 8:
75 goes into 400 5 times with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 1337.05
Deduct 375 from 400 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 9:
75 can be fit into 250 3 times, resulting in a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 1337.053
Subtracting 225 from 250 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 10:
75 can be fit into 250 3 times, resulting in a remainder of 25.
The next digit of our result is 3. 
Result so far: 1337.0533
Subtracting 225 from 250 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 1337.0533, and the remainder is 0.00025.