We're dividing 42769 by 435 
We're looking to find how many times 435 goes into 42769.

Let's proceed to step 1:
The number 435 fits into 4 0 times, leaving a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 435

Let's proceed to step 2:
If we divide 42 by 435, we get 0 and a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 42 leaves us with 42.
Take the next digit (7) from the dividend and append it to 42, then repeat: 427 / 435

Let's proceed to step 3:
If we divide 427 by 435, we get 0 and a remainder of 427.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 427 to get 427.
Take the next digit (6) from the dividend and append it to 427, then repeat: 4276 / 435

Let's proceed to step 4:
4276 divided by 435 is 9 with a remainder of 361.
Write down 9 as next digit of the result. 
Result so far: 9.0
If we take 3915 away from 4276, we end up with 361.
Grab the next digit (9) from the dividend, add it to 361, then carry on: 3619 / 435

On to step 5:
435 can be fit into 3619 8 times, resulting in a remainder of 139.
Use 8 as the next digit of our solution. 
Result so far: 98.0
Subtract 3480 from 3619 to get 139.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1390, and continue the process.

Moving on to step 6:
1390 divided by 435 is 3 with a remainder of 85.
The next digit of our result is 3. 
Result so far: 98.3
Subtract 1305 from 1390 to get 85.
Since there are no more digits in the dividend, we add a zero to the remainder making it 850, and continue the process.

On to step 7:
850 divided by 435 is 1 with a remainder of 415.
Use 1 as the next digit of our solution. 
Result so far: 98.31
Subtracting 435 from 850 leaves us with 415.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4150, and continue the process.

Moving on to step 8:
The number 435 fits into 4150 9 times, leaving a remainder of 235.
Record the quotient 9 as the next digit in the result. 
Result so far: 98.319
If we subtract 3915 from 4150, we get 235.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2350, and continue the process.

Going ahead to step 9:
435 goes into 2350 5 times with a remainder of 175.
The number 5 becomes the next digit in our result. 
Result so far: 98.3195
Subtracting 2175 from 2350 leaves us with 175.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1750, and continue the process.

Advancing to step 10:
If we divide 1750 by 435, we get 4 and a remainder of 10.
Put 4 as the next digit of the answer. 
Result so far: 98.31954
Subtract 1740 from 1750 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 11:
435 goes into 100 0 times with a remainder of 100.
Put 0 as the next digit of the answer. 
Result so far: 98.31954
If we take 0 away from 100, we end up with 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1000, and continue the process.

Step 12:
435 can be fit into 1000 2 times, resulting in a remainder of 130.
Put 2 as the next digit of the answer. 
Result so far: 98.3195402
Subtract 870 from 1000 to get 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1300, and continue the process.

Advancing to step 13:
When dividing 1300 by 435, we get 2 with a remainder of 430.
Record the quotient 2 as the next digit in the result. 
Result so far: 98.31954022
Subtracting 870 from 1300 leaves us with 430.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4300, and continue the process.

After the division, we end up with 98.31954022 and a remainder of 4.3e-07.