We look at the division of 376584 by 54 
Our goal is to divide 376584 by 54.

On to step 1:
3 divided by 54 is 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 54

On to step 2:
37 divided by 54 is 0 with a remainder of 37.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 37, we end up with 37.
Append the next digit (6) from the dividend to 37 and continue with: 376 / 54

On to step 3:
If we divide 376 by 54, we get 6 and a remainder of 52.
Put 6 as the next digit of the answer. 
Result so far: 6.0
The remainder is 52 after subtracting 324 from 376.
Append the next digit (5) from the dividend to 52 and continue with: 525 / 54

On to step 4:
If we divide 525 by 54, we get 9 and a remainder of 39.
Put 9 as the next digit of the answer. 
Result so far: 69.0
The remainder is 39 after subtracting 486 from 525.
Fetch the next digit (8) from the dividend, attach it to 39 and continue: 398 / 54

Step 5:
398 divided by 54 is 7 with a remainder of 20.
Use 7 as the next digit of our solution. 
Result so far: 697.0
The remainder is 20 after subtracting 378 from 398.
Bring next digit (4) of the dividend behind the 20 and repeat the process: 204 / 54

Let's proceed to step 6:
If we divide 204 by 54, we get 3 and a remainder of 42.
The number 3 becomes the next digit in our result. 
Result so far: 6973.0
If we take 162 away from 204, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Step 7:
54 goes into 420 7 times with a remainder of 42.
The number 7 becomes the next digit in our result. 
Result so far: 6973.7
Subtract 378 from 420 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 8:
If we divide 420 by 54, we get 7 and a remainder of 42.
Use 7 as the next digit of our solution. 
Result so far: 6973.77
Subtract 378 from 420 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

The final result is 6973.77 with a remainder of 0.042.