We're dividing 666629 by 79 
We're looking to find how many times 79 goes into 666629.

Step 1:
79 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Append the next digit (6) from the dividend to 6 and continue with: 66 / 79

Advancing to step 2:
If we divide 66 by 79, we get 0 and a remainder of 66.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 66, we end up with 66.
Include the next digit (6) from the dividend after 66, then repeat: 666 / 79

Let's proceed to step 3:
If we divide 666 by 79, we get 8 and a remainder of 34.
The next digit of our result is 8. 
Result so far: 8.0
If we subtract 632 from 666, we get 34.
Grab the next digit (6) from the dividend, add it to 34, then carry on: 346 / 79

Let's proceed to step 4:
346 divided by 79 is 4 with a remainder of 30.
The number 4 becomes the next digit in our result. 
Result so far: 84.0
Subtract 316 from 346 to get 30.
Append the next digit (2) from the dividend to 30 and continue with: 302 / 79

Let's proceed to step 5:
When dividing 302 by 79, we get 3 with a remainder of 65.
Put 3 as the next digit of the answer. 
Result so far: 843.0
If we take 237 away from 302, we end up with 65.
Fetch the next digit (9) from the dividend, attach it to 65 and continue: 659 / 79

Moving on to step 6:
The number 79 fits into 659 8 times, leaving a remainder of 27.
The next digit of our result is 8. 
Result so far: 8438.0
Deduct 632 from 659 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 7:
If we divide 270 by 79, we get 3 and a remainder of 33.
Record the quotient 3 as the next digit in the result. 
Result so far: 8438.3
The remainder is 33 after subtracting 237 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Going ahead to step 8:
79 goes into 330 4 times with a remainder of 14.
The next digit of our result is 4. 
Result so far: 8438.34
If we subtract 316 from 330, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 9:
When dividing 140 by 79, we get 1 with a remainder of 61.
Use 1 as the next digit of our solution. 
Result so far: 8438.341
The remainder is 61 after subtracting 79 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Moving on to step 10:
If we divide 610 by 79, we get 7 and a remainder of 57.
The number 7 becomes the next digit in our result. 
Result so far: 8438.3417
Subtracting 553 from 610 leaves us with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Let's proceed to step 11:
The number 79 fits into 570 7 times, leaving a remainder of 17.
The next digit of our result is 7. 
Result so far: 8438.34177
Deduct 553 from 570 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

The final result is 8438.34177 with a remainder of 1.7e-05.