We divide 4277598 by 659
Our goal is to divide 4277598 by 659.

Advancing to step 1:
If we divide 4 by 659, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 659

Going ahead to step 2:
When dividing 42 by 659, we get 0 with a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Bring next digit (7) of the dividend behind the 42 and repeat the process: 427 / 659

On to step 3:
659 can be fit into 427 0 times, resulting in a remainder of 427.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 427 and we're left with 427.
Fetch the next digit (7) from the dividend, attach it to 427 and continue: 4277 / 659

Moving on to step 4:
The number 659 fits into 4277 6 times, leaving a remainder of 323.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 3954 away from 4277, we end up with 323.
Grab the next digit (5) from the dividend, add it to 323, then carry on: 3235 / 659

Step 5:
The number 659 fits into 3235 4 times, leaving a remainder of 599.
Use 4 as the next digit of our solution. 
Result so far: 64.0
Deduct 2636 from 3235 and we're left with 599.
Grab the next digit (9) from the dividend, add it to 599, then carry on: 5999 / 659

Moving on to step 6:
When dividing 5999 by 659, we get 9 with a remainder of 68.
The next digit of our result is 9. 
Result so far: 649.0
The remainder is 68 after subtracting 5931 from 5999.
Include the next digit (8) from the dividend after 68, then repeat: 688 / 659

On to step 7:
If we divide 688 by 659, we get 1 and a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 6491.0
Deduct 659 from 688 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Let's proceed to step 8:
If we divide 290 by 659, we get 0 and a remainder of 290.
Record the quotient 0 as the next digit in the result. 
Result so far: 6491.0
The remainder is 290 after subtracting 0 from 290.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2900, and continue the process.

On to step 9:
659 can be fit into 2900 4 times, resulting in a remainder of 264.
The number 4 becomes the next digit in our result. 
Result so far: 6491.04
The remainder is 264 after subtracting 2636 from 2900.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2640, and continue the process.

Advancing to step 10:
659 can be fit into 2640 4 times, resulting in a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 6491.044
Subtract 2636 from 2640 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final result is 6491.044 with a remainder of 0.0004.