377741 ÷ 75 
Let's see how many times 75 fits into 377741.

Advancing to step 1:
The number 75 fits into 3 0 times, leaving a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 75

Moving on to step 2:
75 can be fit into 37 0 times, resulting in a remainder of 37.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Take the next digit (7) from the dividend and append it to 37, then repeat: 377 / 75

Advancing to step 3:
If we divide 377 by 75, we get 5 and a remainder of 2.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtract 375 from 377 to get 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 75

Let's proceed to step 4:
75 goes into 27 0 times with a remainder of 27.
The next digit of our result is 0. 
Result so far: 50.0
If we subtract 0 from 27, we get 27.
Bring next digit (4) of the dividend behind the 27 and repeat the process: 274 / 75

On to step 5:
274 divided by 75 is 3 with a remainder of 49.
Record the quotient 3 as the next digit in the result. 
Result so far: 503.0
Subtract 225 from 274 to get 49.
Take the next digit (1) from the dividend and append it to 49, then repeat: 491 / 75

Step 6:
75 goes into 491 6 times with a remainder of 41.
Put 6 as the next digit of the answer. 
Result so far: 5036.0
The remainder is 41 after subtracting 450 from 491.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

On to step 7:
When dividing 410 by 75, we get 5 with a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 5036.5
If we take 375 away from 410, we end up 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.

Let's proceed to step 8:
75 goes into 350 4 times with a remainder of 50.
The number 4 becomes the next digit in our result. 
Result so far: 5036.54
Subtract 300 from 350 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 9:
When dividing 500 by 75, we get 6 with a remainder of 50.
Put 6 as the next digit of the answer. 
Result so far: 5036.546
If we take 450 away from 500, 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.

Going ahead to step 10:
If we divide 500 by 75, we get 6 and a remainder of 50.
The next digit of our result is 6. 
Result so far: 5036.5466
If we subtract 450 from 500, we get 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 5036.5466, and the remainder is 0.0005.