278966 ÷ 75 
We're looking to find how many times 75 goes into 278966.

Step 1:
When dividing 2 by 75, we get 0 with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 75

Let's proceed to step 2:
If we divide 27 by 75, we get 0 and a remainder of 27.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 27 to get 27.
Fetch the next digit (8) from the dividend, attach it to 27 and continue: 278 / 75

On to step 3:
If we divide 278 by 75, we get 3 and a remainder of 53.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 225 from 278, we get 53.
Take the next digit (9) from the dividend and append it to 53, then repeat: 539 / 75

Let's proceed to step 4:
When dividing 539 by 75, we get 7 with a remainder of 14.
Use 7 as the next digit of our solution. 
Result so far: 37.0
Subtracting 525 from 539 leaves us with 14.
Grab the next digit (6) from the dividend, add it to 14, then carry on: 146 / 75

Moving on to step 5:
75 can be fit into 146 1 times, resulting in a remainder of 71.
Use 1 as the next digit of our solution. 
Result so far: 371.0
If we subtract 75 from 146, we get 71.
Take the next digit (6) from the dividend and append it to 71, then repeat: 716 / 75

Moving on to step 6:
If we divide 716 by 75, we get 9 and a remainder of 41.
The number 9 becomes the next digit in our result. 
Result so far: 3719.0
If we take 675 away from 716, we end up with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Moving on to step 7:
The number 75 fits into 410 5 times, leaving a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 3719.5
Deduct 375 from 410 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 8:
75 can be fit into 350 4 times, resulting in a remainder of 50.
Use 4 as the next digit of our solution. 
Result so far: 3719.54
The remainder is 50 after subtracting 300 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Let's proceed to step 9:
If we divide 500 by 75, we get 6 and a remainder of 50.
The number 6 becomes the next digit in our result. 
Result so far: 3719.546
Subtracting 450 from 500 leaves us 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.

On to step 10:
75 goes into 500 6 times with a remainder of 50.
Write down 6 as next digit of the result. 
Result so far: 3719.5466
The remainder is 50 after subtracting 450 from 500.
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 3719.5466, and the remainder is 0.0005.