377503 ÷ 90 
We want to divide 377503 by 90.

Advancing to step 1:
90 goes into 3 0 times with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Include the next digit (7) from the dividend after 3, then repeat: 37 / 90

On to step 2:
90 can be fit into 37 0 times, resulting in a remainder of 37.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 37 leaves us with 37.
Fetch the next digit (7) from the dividend, attach it to 37 and continue: 377 / 90

On to step 3:
90 goes into 377 4 times with a remainder of 17.
The next digit of our result is 4. 
Result so far: 4.0
If we take 360 away from 377, we end up with 17.
Append the next digit (5) from the dividend to 17 and continue with: 175 / 90

Let's proceed to step 4:
The number 90 fits into 175 1 times, leaving a remainder of 85.
Use 1 as the next digit of our solution. 
Result so far: 41.0
Subtracting 90 from 175 leaves us with 85.
Append the next digit (0) from the dividend to 85 and continue with: 850 / 90

Let's proceed to step 5:
The number 90 fits into 850 9 times, leaving a remainder of 40.
The number 9 becomes the next digit in our result. 
Result so far: 419.0
Subtracting 810 from 850 leaves us with 40.
Fetch the next digit (3) from the dividend, attach it to 40 and continue: 403 / 90

Let's proceed to step 6:
If we divide 403 by 90, we get 4 and a remainder of 43.
Record the quotient 4 as the next digit in the result. 
Result so far: 4194.0
Deduct 360 from 403 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 7:
When dividing 430 by 90, we get 4 with a remainder of 70.
Record the quotient 4 as the next digit in the result. 
Result so far: 4194.4
Subtracting 360 from 430 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 8:
700 divided by 90 is 7 with a remainder of 70.
The number 7 becomes the next digit in our result. 
Result so far: 4194.47
If we take 630 away from 700, we end up with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Advancing to step 9:
The number 90 fits into 700 7 times, leaving a remainder of 70.
The next digit of our result is 7. 
Result so far: 4194.477
The remainder is 70 after subtracting 630 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

After the division, we end up with 4194.477 and a remainder of 0.007.