We're dividing 357778 by 35 
Let's see how many times 35 fits into 357778.

Going ahead to step 1:
When dividing 3 by 35, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 35

On to step 2:
35 goes into 35 1 times with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 35 from 35 leaves us with 0.
Grab the next digit (7) from the dividend, add it to 0, then carry on: 7 / 35

Let's proceed to step 3:
If we divide 7 by 35, we get 0 and a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Subtracting 0 from 7 leaves us with 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 35

Going ahead to step 4:
When dividing 77 by 35, we get 2 with a remainder of 7.
Put 2 as the next digit of the answer. 
Result so far: 102.0
Subtracting 70 from 77 leaves us with 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 35

Let's proceed to step 5:
77 divided by 35 is 2 with a remainder of 7.
Use 2 as the next digit of our solution. 
Result so far: 1022.0
If we take 70 away from 77, we end up with 7.
Append the next digit (8) from the dividend to 7 and continue with: 78 / 35

Advancing to step 6:
If we divide 78 by 35, we get 2 and a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 10222.0
If we take 70 away from 78, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 7:
If we divide 80 by 35, we get 2 and a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 10222.2
If we subtract 70 from 80, we 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.

Moving on to step 8:
35 goes into 100 2 times with a remainder of 30.
Use 2 as the next digit of our solution. 
Result so far: 10222.22
If we take 70 away from 100, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The final result is 10222.22 with a remainder of 0.03.