We look at the division of 66235679 by 434 
We want to figure out the number of times 66235679 can be divided by 434.

Advancing to step 1:
If we divide 6 by 434, we get 0 and a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 434

Moving on to step 2:
434 can be fit into 66 0 times, resulting in a remainder of 66.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 66 and we're left with 66.
Include the next digit (2) from the dividend after 66, then repeat: 662 / 434

Moving on to step 3:
434 can be fit into 662 1 times, resulting in a remainder of 228.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 434 from 662 to get 228.
Grab the next digit (3) from the dividend, add it to 228, then carry on: 2283 / 434

Let's proceed to step 4:
434 goes into 2283 5 times with a remainder of 113.
Put 5 as the next digit of the answer. 
Result so far: 15.0
Deduct 2170 from 2283 and we're left with 113.
Append the next digit (5) from the dividend to 113 and continue with: 1135 / 434

On to step 5:
1135 divided by 434 is 2 with a remainder of 267.
Record the quotient 2 as the next digit in the result. 
Result so far: 152.0
Deduct 868 from 1135 and we're left with 267.
Include the next digit (6) from the dividend after 267, then repeat: 2676 / 434

Let's proceed to step 6:
2676 divided by 434 is 6 with a remainder of 72.
Use 6 as the next digit of our solution. 
Result so far: 1526.0
Deduct 2604 from 2676 and we're left with 72.
Grab the next digit (7) from the dividend, add it to 72, then carry on: 727 / 434

Let's proceed to step 7:
727 divided by 434 is 1 with a remainder of 293.
Use 1 as the next digit of our solution. 
Result so far: 15261.0
Deduct 434 from 727 and we're left with 293.
Bring next digit (9) of the dividend behind the 293 and repeat the process: 2939 / 434

Going ahead to step 8:
The number 434 fits into 2939 6 times, leaving a remainder of 335.
Use 6 as the next digit of our solution. 
Result so far: 152616.0
Deduct 2604 from 2939 and we're left with 335.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3350, and continue the process.

Going ahead to step 9:
When dividing 3350 by 434, we get 7 with a remainder of 312.
Put 7 as the next digit of the answer. 
Result so far: 152616.7
If we subtract 3038 from 3350, we get 312.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3120, and continue the process.

Advancing to step 10:
434 goes into 3120 7 times with a remainder of 82.
The next digit of our result is 7. 
Result so far: 152616.77
If we take 3038 away from 3120, we end up with 82.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

The quotient of the division is 152616.77, and the remainder is 0.082.