We're dividing 377966 by 583 
Our goal is to divide 377966 by 583.

Let's proceed to step 1:
If we divide 3 by 583, we get 0 and a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 583

On to step 2:
583 goes into 37 0 times with a remainder of 37.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 37, we get 37.
Append the next digit (7) from the dividend to 37 and continue with: 377 / 583

Going ahead to step 3:
The number 583 fits into 377 0 times, leaving a remainder of 377.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 377 to get 377.
Include the next digit (9) from the dividend after 377, then repeat: 3779 / 583

Advancing to step 4:
The number 583 fits into 3779 6 times, leaving a remainder of 281.
Write down 6 as next digit of the result. 
Result so far: 6.0
Subtract 3498 from 3779 to get 281.
Bring next digit (6) of the dividend behind the 281 and repeat the process: 2816 / 583

Going ahead to step 5:
2816 divided by 583 is 4 with a remainder of 484.
The number 4 becomes the next digit in our result. 
Result so far: 64.0
Subtract 2332 from 2816 to get 484.
Grab the next digit (6) from the dividend, add it to 484, then carry on: 4846 / 583

Advancing to step 6:
If we divide 4846 by 583, we get 8 and a remainder of 182.
Write down 8 as next digit of the result. 
Result so far: 648.0
If we subtract 4664 from 4846, we get 182.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1820, and continue the process.

Going ahead to step 7:
The number 583 fits into 1820 3 times, leaving a remainder of 71.
The next digit of our result is 3. 
Result so far: 648.3
Subtract 1749 from 1820 to get 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Going ahead to step 8:
710 divided by 583 is 1 with a remainder of 127.
The next digit of our result is 1. 
Result so far: 648.31
If we subtract 583 from 710, we get 127.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1270, and continue the process.

Step 9:
583 goes into 1270 2 times with a remainder of 104.
The next digit of our result is 2. 
Result so far: 648.312
If we take 1166 away from 1270, we end up with 104.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1040, and continue the process.

On to step 10:
1040 divided by 583 is 1 with a remainder of 457.
Record the quotient 1 as the next digit in the result. 
Result so far: 648.3121
Subtracting 583 from 1040 leaves us with 457.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4570, and continue the process.

Step 11:
583 goes into 4570 7 times with a remainder of 489.
Use 7 as the next digit of our solution. 
Result so far: 648.31217
Subtracting 4081 from 4570 leaves us with 489.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4890, and continue the process.

Advancing to step 12:
4890 divided by 583 is 8 with a remainder of 226.
The number 8 becomes the next digit in our result. 
Result so far: 648.312178
The remainder is 226 after subtracting 4664 from 4890.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2260, and continue the process.

Advancing to step 13:
If we divide 2260 by 583, we get 3 and a remainder of 511.
The number 3 becomes the next digit in our result. 
Result so far: 648.3121783
Deduct 1749 from 2260 and we're left with 511.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5110, and continue the process.

Step 14:
If we divide 5110 by 583, we get 8 and a remainder of 446.
The next digit of our result is 8. 
Result so far: 648.31217838
Subtract 4664 from 5110 to get 446.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4460, and continue the process.

The final outcome is 648.31217838, with a leftover of 4.46e-07.