554778 ÷ 137 
Our goal is to divide 554778 by 137.

Going ahead to step 1:
When dividing 5 by 137, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 137

Advancing to step 2:
137 goes into 55 0 times with a remainder of 55.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 55 leaves us with 55.
Append the next digit (4) from the dividend to 55 and continue with: 554 / 137

Going ahead to step 3:
137 goes into 554 4 times with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 4.0
Subtracting 548 from 554 leaves us with 6.
Grab the next digit (7) from the dividend, add it to 6, then carry on: 67 / 137

On to step 4:
137 can be fit into 67 0 times, resulting in a remainder of 67.
The next digit of our result is 0. 
Result so far: 40.0
Subtract 0 from 67 to get 67.
Grab the next digit (7) from the dividend, add it to 67, then carry on: 677 / 137

Advancing to step 5:
When dividing 677 by 137, we get 4 with a remainder of 129.
The number 4 becomes the next digit in our result. 
Result so far: 404.0
If we subtract 548 from 677, we get 129.
Fetch the next digit (8) from the dividend, attach it to 129 and continue: 1298 / 137

Moving on to step 6:
The number 137 fits into 1298 9 times, leaving a remainder of 65.
Use 9 as the next digit of our solution. 
Result so far: 4049.0
If we take 1233 away from 1298, we end up with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Let's proceed to step 7:
The number 137 fits into 650 4 times, leaving a remainder of 102.
The number 4 becomes the next digit in our result. 
Result so far: 4049.4
Subtracting 548 from 650 leaves us with 102.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1020, and continue the process.

Step 8:
The number 137 fits into 1020 7 times, leaving a remainder of 61.
Use 7 as the next digit of our solution. 
Result so far: 4049.47
Subtracting 959 from 1020 leaves us with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Going ahead to step 9:
137 can be fit into 610 4 times, resulting in a remainder of 62.
Use 4 as the next digit of our solution. 
Result so far: 4049.474
The remainder is 62 after subtracting 548 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 10:
The number 137 fits into 620 4 times, leaving a remainder of 72.
Put 4 as the next digit of the answer. 
Result so far: 4049.4744
If we subtract 548 from 620, we get 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

The quotient of the division is 4049.4744, and the remainder is 0.00072.